Introduction to Global Analysis

Author: Donald W. Kahn

Publisher: Courier Corporation

ISBN: 9780486152295

Category: Mathematics

Page: 352

View: 6560

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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.
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Introduction to Global Analysis: Minimal Surfaces in Riemannian Manifolds

Author: John Douglas Moore

Publisher: American Mathematical Soc.

ISBN: 1470429500

Category: Electronic books

Page: 368

View: 1124

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During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed parametrized minimal surfaces in a compact Riemannian manifold, establishing Morse inequalities for perturbed versions of the energy function on the mapping space. It studies the bubbling which occurs when the perturbation is turned off, together with applications to the existence of closed minimal surfaces. The Morse-Sard theorem is used to develop transversality theory for both closed geodesics and closed minimal surfaces. This book is based on lecture notes for graduate courses on “Topics in Differential Geometry”, taught by the author over several years. The reader is assumed to have taken basic graduate courses in differential geometry and algebraic topology.
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Global Analysis of Dynamical Systems

Festschrift dedicated to Floris Takens for his 60th birthday

Author: H.W Broer,B Krauskopf,Gert Vegter

Publisher: CRC Press

ISBN: 9781420034288

Category: Mathematics

Page: 464

View: 3596

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Contributed by close colleagues, friends, and former students of Floris Takens, Global Analysis of Dynamical Systems is a liber amicorum dedicated to Takens for his 60th birthday. The first chapter is a reproduction of Takens's 1974 paper "Forced oscillators and bifurcations" that was previously available only as a preprint of the University of Utrecht. Among other important results, it contains the unfolding of what is now known as the Bogdanov-Takens bifurcation. The remaining chapters cover topics as diverse as bifurcation theory, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic theory, renormalization theory, and time series analysis. In its entirety, the book bears witness to the influence of Takens on the modern theory of dynamical systems and its applications. This book is a must-read for anyone interested in this active and exciting field.
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Handbook of Global Analysis

Author: Demeter Krupka,David Saunders

Publisher: Elsevier

ISBN: 9780080556734

Category: Mathematics

Page: 1244

View: 9973

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This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics. This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics - Written by world-experts in the field - Up-to-date contents
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Nonlinear and Global Analysis

Author: Felix E. Browder

Publisher: American Mathematical Soc.

ISBN: 9780821888544

Category: Mathematics

Page: 625

View: 9537

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This volume contains a number of research-expository articles that appeared in the Bulletin of the AMS between 1979 and 1984 and that address the general area of nonlinear functional analysis and global analysis and their applications. The central theme concerns qualitative methods in the study of nonlinear problems arising in applied mathematics, mathematical physics, and geometry. Since these articles first appeared, the methods and ideas they describe have been applied in an ever-widening array of applications. Readers will find this collection useful, as it brings together a range of influential papers by some of the leading researchers in the field.
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Introduction to Global Variational Geometry

Author: Demeter Krupka

Publisher: Elsevier

ISBN: 9780080954271

Category: Mathematics

Page: 500

View: 6709

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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Euler-Lagrange mapping - Helmholtz form and the inverse problem - Symmetries and the Noether’s theory of conservation laws - Regularity and the Hamilton theory - Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces
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Lectures on Dynamical Systems, Structural Stability, and Their Applications

Author: Kotik K. Lee

Publisher: World Scientific

ISBN: 9789971509651

Category: Science

Page: 454

View: 1153

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The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.
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Strengths and Weaknesses in Securities Market Regulation: A Global Analysis

Author: Ana Carvajal,Jennifer A. Elliott

Publisher: International Monetary Fund

ISBN: N.A

Category: Economic policy

Page: 49

View: 6032

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This paper examines the strengths and weaknesses of securities regulatory systems worldwide with a view to a better understanding of common problems and areas of global concern. We found that a consistent theme emerges regarding the lack of ability of regulators to effectively enforce compliance with existing rules and regulation. In many countries, a combination of factors, including insufficient legal authority, a lack of resources, political will and skills, has undermined the regulator's capacity to effectively execute regulation. This weakness is more acute in areas of increased technical complexity such as standards for and supervision of the valuation of assets and risk management practices.
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