Dynamical Systems

Dynamical Systems

A pioneer in the field of dynamical systems discusses one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains.

Author: Shlomo Sternberg

Publisher: Courier Corporation

ISBN: 9780486135144

Category: Mathematics

Page: 272

View: 436

A pioneer in the field of dynamical systems discusses one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials include PowerPoint slides and MATLAB exercises. 2010 edition.
Categories: Mathematics

Invitation to Dynamical Systems

Invitation to Dynamical Systems

This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material.

Author: Edward R. Scheinerman

Publisher: Courier Corporation

ISBN: 9780486275321

Category: Mathematics

Page: 408

View: 254

This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.
Categories: Mathematics

Dynamical Systems by Example

Dynamical Systems by Example

This book comprises an impressive collection of problems that cover a variety of carefully selected topics on the core of the theory of dynamical systems.

Author: Luís Barreira

Publisher: Springer

ISBN: 3030159140

Category: Mathematics

Page: 223

View: 319

This book comprises an impressive collection of problems that cover a variety of carefully selected topics on the core of the theory of dynamical systems. Aimed at the graduate/upper undergraduate level, the emphasis is on dynamical systems with discrete time. In addition to the basic theory, the topics include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as basic ergodic theory. As in other areas of mathematics, one can gain the first working knowledge of a topic by solving selected problems. It is rare to find large collections of problems in an advanced field of study much less to discover accompanying detailed solutions. This text fills a gap and can be used as a strong companion to an analogous dynamical systems textbook such as the authors’ own Dynamical Systems (Universitext, Springer) or another text designed for a one- or two-semester advanced undergraduate/graduate course. The book is also intended for independent study. Problems often begin with specific cases and then move on to general results, following a natural path of learning. They are also well-graded in terms of increasing the challenge to the reader. Anyone who works through the theory and problems in Part I will have acquired the background and techniques needed to do advanced studies in this area. Part II includes complete solutions to every problem given in Part I with each conveniently restated. Beyond basic prerequisites from linear algebra, differential and integral calculus, and complex analysis and topology, in each chapter the authors recall the notions and results (without proofs) that are necessary to treat the challenges set for that chapter, thus making the text self-contained.
Categories: Mathematics

Qualitative Theory of Differential Equations

Qualitative Theory of Differential Equations

Graduate-level text considers existence and continuity theorems, integral curves of a system of 2 differential equations, systems of n-differential equations, general theory of dynamical systems, systems with an integral invariant, more. ...

Author: V. V. Nemytskii

Publisher: Courier Corporation

ISBN: 0486659542

Category: Mathematics

Page: 523

View: 493

Graduate-level text considers existence and continuity theorems, integral curves of a system of 2 differential equations, systems of n-differential equations, general theory of dynamical systems, systems with an integral invariant, more. 1960 edition.
Categories: Mathematics

A Mathematical Companion to Quantum Mechanics

A Mathematical Companion to Quantum Mechanics

This original 2019 work, based on the author's many years of teaching at Harvard University, examines mathematical methods of value and importance to advanced undergraduates and graduate students studying quantum mechanics.

Author: Shlomo Sternberg

Publisher: Courier Dover Publications

ISBN: 9780486826899

Category: Science

Page: 336

View: 610

This original 2019 work, based on the author's many years of teaching at Harvard University, examines mathematical methods of value and importance to advanced undergraduates and graduate students studying quantum mechanics. Its intended audience is students of mathematics at the senor university level and beginning graduate students in mathematics and physics. Early chapters address such topics as the Fourier transform, the spectral theorem for bounded self-joint operators, and unbounded operators and semigroups. Subsequent topics include a discussion of Weyl's theorem on the essential spectrum and some of its applications, the Rayleigh-Ritz method, one-dimensional quantum mechanics, Ruelle's theorem, scattering theory, Huygens' principle, and many other subjects.
Categories: Science

The Art of Modeling Dynamic Systems

The Art of Modeling Dynamic Systems

The original edition was a Library of Science Main Selection in May, 1991. This new Dover edition features corrections by the author and a new Preface.

Author: Foster Morrison

Publisher: Courier Corporation

ISBN: 9780486131719

Category: Mathematics

Page: 416

View: 971

This text illustrates the roles of statistical methods, coordinate transformations, and mathematical analysis in mapping complex, unpredictable dynamical systems. It describes the benefits and limitations of the available modeling tools, showing engineers and scientists how any system can be rendered simpler and more predictable. Written by a well-known authority in the field, this volume employs practical examples and analogies to make models more meaningful. The more universal methods appear in considerable detail, and advanced dynamic principles feature easy-to-understand examples. The text draws careful distinctions between mathematical abstractions and observable realities. Additional topics include the role of pure mathematics, the limitations of numerical methods, forecasting in the presence of chaos and randomness, and dynamics without calculus. Specialized techniques and case histories are coordinated with a carefully selected and annotated bibliography. The original edition was a Library of Science Main Selection in May, 1991. This new Dover edition features corrections by the author and a new Preface.
Categories: Mathematics

Introduction to Global Analysis

Introduction to Global Analysis

This text introduces the methods of mathematical analysis as applied to manifolds, including the roles of differentiation and integration, infinite dimensions, Morse theory, Lie groups, and dynamical systems. 1980 edition.

Author: Donald W. Kahn

Publisher: Courier Corporation

ISBN: 0486152294

Category: Mathematics

Page: 352

View: 787

This text introduces the methods of mathematical analysis as applied to manifolds, including the roles of differentiation and integration, infinite dimensions, Morse theory, Lie groups, and dynamical systems. 1980 edition.
Categories: Mathematics

Dynamic Probabilistic Systems

Dynamic Probabilistic Systems

An integrated work in two volumes, this text teaches readers to formulate, analyze, and evaluate Markov models. The first volume treats basic process; the second, semi-Markov and decision processes. 1971 edition.

Author: Ronald A. Howard

Publisher: Courier Corporation

ISBN: 9780486140674

Category: Mathematics

Page: 608

View: 949

An integrated work in two volumes, this text teaches readers to formulate, analyze, and evaluate Markov models. The first volume treats basic process; the second, semi-Markov and decision processes. 1971 edition.
Categories: Mathematics

Analysis and Control of Complex Dynamical Systems

Analysis and Control of Complex Dynamical Systems

Dover Books on Mathematics. Dover Publications, New York (1997) MacKay, R.: A simple proof of Denjoy's theorem. Math. Proc. Cambridge Philos. Soc.

Author: Kazuyuki Aihara

Publisher: Springer

ISBN: 9784431550136

Category: Technology & Engineering

Page: 211

View: 558

This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems.
Categories: Technology & Engineering

Optimal Control and Estimation

Optimal Control and Estimation

Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.

Author: Robert F. Stengel

Publisher: Courier Corporation

ISBN: 9780486134819

Category: Mathematics

Page: 672

View: 969

Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.
Categories: Mathematics

Ergodic Theory and Dynamical Systems

Ergodic Theory and Dynamical Systems

Dover Books on Advanced Mathematics. Dover Publications Inc., New York (1990) 20. Rohlin, V.A.: On the Fundamental Ideas of Measure Theory.

Author: Yves Coudène

Publisher: Springer

ISBN: 9781447172871

Category: Mathematics

Page: 190

View: 112

This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.
Categories: Mathematics

Stable and Efficient Cubature based Filtering in Dynamical Systems

Stable and Efficient Cubature based Filtering in Dynamical Systems

Dover books on engineering. Mineola, NY: Dover Publications. ... Mathematical description of linear dynamical systems. Journal of the Society for Industrial ...

Author: Dominik Ballreich

Publisher: Springer

ISBN: 9783319621302

Category: Business & Economics

Page: 160

View: 352

The book addresses the problem of calculation of d-dimensional integrals (conditional expectations) in filter problems. It develops new methods of deterministic numerical integration, which can be used to speed up and stabilize filter algorithms. With the help of these methods, better estimates and predictions of latent variables are made possible in the fields of economics, engineering and physics. The resulting procedures are tested within four detailed simulation studies.
Categories: Business & Economics

Dynamic Probabilistic Systems

Dynamic Probabilistic Systems

An integrated work in two volumes, this text teaches readers to formulate, analyze, and evaluate Markov models. The first volume treats the basic process; the second, semi-Markov and decision processes. 1971 edition.

Author: Ronald A. Howard

Publisher: Courier Corporation

ISBN: 9780486152004

Category: Mathematics

Page: 576

View: 208

An integrated work in two volumes, this text teaches readers to formulate, analyze, and evaluate Markov models. The first volume treats the basic process; the second, semi-Markov and decision processes. 1971 edition.
Categories: Mathematics

Optimal Trajectory Tracking of Nonlinear Dynamical Systems

Optimal Trajectory Tracking of Nonlinear Dynamical Systems

(Dover Publications, Mineola, 2003). ... ISBN 9780387758466 J. Keener, J. Sneyd,Mathematical Physiology: II: Systems Physiology.

Author: Jakob Löber

Publisher: Springer

ISBN: 9783319465746

Category: Science

Page: 243

View: 108

By establishing an alternative foundation of control theory, this thesis represents a significant advance in the theory of control systems, of interest to a broad range of scientists and engineers. While common control strategies for dynamical systems center on the system state as the object to be controlled, the approach developed here focuses on the state trajectory. The concept of precisely realizable trajectories identifies those trajectories that can be accurately achieved by applying appropriate control signals. The resulting simple expressions for the control signal lend themselves to immediate application in science and technology. The approach permits the generalization of many well-known results from the control theory of linear systems, e.g. the Kalman rank condition to nonlinear systems. The relationship between controllability, optimal control and trajectory tracking are clarified. Furthermore, the existence of linear structures underlying nonlinear optimal control is revealed, enabling the derivation of exact analytical solutions to an entire class of nonlinear optimal trajectory tracking problems. The clear and self-contained presentation focuses on a general and mathematically rigorous analysis of controlled dynamical systems. The concepts developed are visualized with the help of particular dynamical systems motivated by physics and chemistry.
Categories: Science

Differential Calculus and Its Applications

Differential Calculus and Its Applications

Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition ...

Author: Michael J. Field

Publisher: Courier Corporation

ISBN: 9780486298849

Category: Mathematics

Page: 336

View: 292

Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.
Categories: Mathematics

Complex Analysis and Dynamical Systems VI

Complex Analysis and Dynamical Systems VI

MR3184618 P. Koosis, Introduction to Hp spaces, London Mathematical Society ... Theory and their Application to Mathematical Physics, Dover Publications, ...

Author: Lawrence Zalcman

Publisher: American Mathematical Soc.

ISBN: 9781470417031

Category: Calculus of variations

Page: 316

View: 828

This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19–24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers range over a wide variety of topics in complex analysis, quasiconformal mappings, and complex dynamics. Taken together, the articles provide the reader with a panorama of activity in these areas, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 653) is devoted to partial differential equations, differential geometry, and radon transforms.
Categories: Calculus of variations

Mathematics of Complexity and Dynamical Systems

Mathematics of Complexity and Dynamical Systems

Courier Dover Publications, 288 pp Kuksin SB (1988) Perturbation theory of conditionally periodic solutions of infinite-dimensional Hamiltonian systems and ...

Author: Robert A. Meyers

Publisher: Springer Science & Business Media

ISBN: 9781461418054

Category: Mathematics

Page: 1858

View: 369

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Categories: Mathematics

Substitution Dynamical Systems Spectral Analysis

Substitution Dynamical Systems   Spectral Analysis

T. KAMAE, Mutual singularity of spectra of dynamical systems given by sums of ... Uniform distribution of sequences, Dover Publications, Inc., New York, ...

Author: Martine Queffélec

Publisher: Springer

ISBN: 9783642112126

Category: Mathematics

Page: 351

View: 380

This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.
Categories: Mathematics

An Introduction to Dynamical Systems and Chaos

An Introduction to Dynamical Systems and Chaos

Springer-Verlag (1982) Bahi, J.M., Guyeux, C.: Discrete Dynamical Systems and ... transition to turbulence in dissipative dynamical systems. Commun. Math.

Author: G.C. Layek

Publisher: Springer

ISBN: 9788132225560

Category: Mathematics

Page: 622

View: 705

The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.
Categories: Mathematics

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics Fractals in pure mathematics

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics  Fractals in pure mathematics

Math. Phys. 183 (1997), no. 1, 85–117, DOI 10.1007/BF02509797. ... Operator Methods in Quantum Mechanics, Dover Publications Inc., Mineola, NY, 2002.

Author: David Carfi

Publisher: American Mathematical Soc.

ISBN: 9780821891476

Category: Mathematics

Page: 399

View: 120

This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.
Categories: Mathematics