On Some Aspects of the Theory of Anosov Systems

With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows

Author: Grigorii A. Margulis

Publisher: Springer Science & Business Media

ISBN: 3662090708

Category: Mathematics

Page: 144

View: 9599

The seminal 1970 Moscow thesis of Grigoriy A. Margulis, published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing.
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Cohomological Theory of Dynamical Zeta Functions

Author: Andreas Juhl

Publisher: Birkhäuser

ISBN: 3034883404

Category: Mathematics

Page: 709

View: 8852

Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions. The present book is concerned with these zeta functions from a cohomological point of view. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were suggested by an analogy between Weil's explicit formula for the Riemann zeta function and Selberg's trace formula ([261]). The purpose of the cohomological theory is to understand the analytical properties of the zeta functions on the basis of suitable analogs of the Lefschetz fixed point formula in which periodic orbits of the geodesic flow take the place of fixed points. This approach is parallel to Weil's idea to analyze the zeta functions of pro jective algebraic varieties over finite fields on the basis of suitable versions of the Lefschetz fixed point formula. The Lefschetz formula formalism shows that the divisors of the rational Hassc-Wcil zeta functions are determined by the spectra of Frobenius operators on l-adic cohomology.
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Algebraic Groups

Author: Yuri Tschinkel

Publisher: Universitätsverlag Göttingen

ISBN: 3938616776

Category: Algebraic varieties

Page: 155

View: 3433

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Documenta Mathematica

Journal Der Deutschen Mathematiker-Vereinigung

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1588

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International Mathematical News

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1655

Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.
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Forthcoming Books

Author: Rose Arny

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 4545

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First European Congress of Mathematics Paris, July 6–10, 1992

Vol. II: Invited Lectures

Author: Anthony Joseph,Fulbert Mignot,Francois Murat,Bernard Prum,Rudolf Rentschler

Publisher: Birkhäuser

ISBN: 3034891121

Category: Mathematics

Page: 513

View: 3116

Table of Contents: D. Duffie: Martingales, Arbitrage, and Portfolio Choice J. Frhlich: Mathematical Aspects of the Quantum Hall Effect M. Giaquinta: Analytic and Geometric Aspects of Variational Problems for Vector Valued Mappings U. Hamenstdt: Harmonic Measures for Leafwise Elliptic Operators Along Foliations M. Kontsevich: Feynman Diagrams and Low-Dimensional Topology S.B. Kuksin: KAM-Theory for Partial Differential Equations M. Laczkovich: Paradoxical Decompositions: A Survey of Recent Results J.-F. Le Gall: A Path-Valued Markov Process and its Connections with Partial Differential Equations I. Madsen: The Cyclotomic Trace in Algebraic K-Theory A.S. Merkurjev: Algebraic K-Theory and Galois Cohomology J. Nekovr: Values of L-Functions and p-Adic Cohomology Y.A. Neretin: Mantles, Trains and Representations of Infinite Dimensional Groups M.A. Nowak: The Evolutionary Dynamics of HIV Infections R. Piene: On the Enumeration of Algebraic Curves - from Circles to Instantons A. Quarteroni: Mathematical Aspects of Domain Decomposition Methods A. Schrijver: Paths in Graphs and Curves on Surfaces B. Silverman: Function Estimation and Functional Data Analysis V. Strassen: Algebra and Complexity P. Tukia: Generalizations of Fuchsian and Kleinian Groups C. Viterbo: Properties of Embedded Lagrange Manifolds D. Voiculescu: Alternative Entropies in Operator Algebras M. Wodzicki : Algebraic K-Theory and Functional Analysis D. Zagier: Values of Zeta Functions and Their Applications.
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Modern Mathematics in the Light of the Fields Medals

Author: Michael Monastyrsky

Publisher: A K Peters/CRC Press

ISBN: N.A

Category: Mathematics

Page: 176

View: 8619

This small book demonstrates the evolution of certain areas of modern mathematics by examining the work of past winners of the Fields Medal, the "Nobel Prize" of mathematics. Foreword by Freeman Dyson.
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Open Problems in Mathematics

Author: John Forbes Nash, Jr.,Michael Th. Rassias

Publisher: Springer

ISBN: 3319321625

Category: Mathematics

Page: 543

View: 1792

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.
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Mathematical Physics X

Proceedings of the Xth Congress on Mathematical Physics, Held at Leipzig, Germany, 30 July – 9 August, 1991

Author: Konrad Schmüdgen

Publisher: Springer Science & Business Media

ISBN: 3642773036

Category: Science

Page: 497

View: 3189

The plenary lectures in this volume give a fairly complete overview of present research in mathematical physics. The contributions cover classical mechanics on manifolds, non-commutative differential geometry and quantum groups, chaotic quantum systems, various topics in equilibrium and non-equilibrium statistical mechanics, quantum field theory, including topological field theory, and classical field theory.
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Issues in General and Specialized Mathematics Research: 2011 Edition

Author: N.A

Publisher: ScholarlyEditions

ISBN: 1464964920

Category: Mathematics

Page: 862

View: 7321

Issues in General and Specialized Mathematics Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General and Specialized Mathematics Research. The editors have built Issues in General and Specialized Mathematics Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General and Specialized Mathematics Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
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