Geometric and Probabilistic Structures in Dynamics
Geometric and Probabilistic Structures in Dynamics

Author: Keith Burns

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 358

ISBN-13: 0821842862

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"This book presents a collection of articles that cover areas of mathematics related to dynamical systems. The authors are well-known experts who use geometric and probabilistic methods to study interesting problems in the theory of dynamical systems and its applications. Some of the articles are surveys while others are original contributions. The topics covered include: Riemannian geometry, models in mathematical physics and mathematical biology, symbolic dynamics, random and stochastic dynamics. This book can be used by graduate students and researchers in dynamical systems and its applications."--BOOK JACKET.

Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
Analytic and Probabilistic Approaches to Dynamics in Negative Curvature

Author: Françoise Dal'Bo

Publisher: Springer

Published: 2014-07-17

Total Pages: 148

ISBN-13: 3319048074

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The work consists of two introductory courses, developing different points of view on the study of the asymptotic behaviour of the geodesic flow, namely: the probabilistic approach via martingales and mixing (by Stéphane Le Borgne); the semi-classical approach, by operator theory and resonances (by Frédéric Faure and Masato Tsujii). The contributions aim to give a self-contained introduction to the ideas behind the three different approaches to the investigation of hyperbolic dynamics. The first contribution focus on the convergence towards a Gaussian law of suitably normalized ergodic sums (Central Limit Theorem). The second one deals with Transfer Operators and the structure of their spectrum (Ruelle-Pollicott resonances), explaining the relation with the asymptotics of time correlation function and the periodic orbits of the dynamics.

Dimension Groups and Dynamical Systems
Dimension Groups and Dynamical Systems

Author: Fabien Durand

Publisher: Cambridge University Press

Published: 2022-02-03

Total Pages: 593

ISBN-13: 1108838685

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This is the first self-contained exposition of the connections between symbolic dynamical systems, dimension groups and Bratteli diagrams.

Foliations, Geometry, and Topology
Foliations, Geometry, and Topology

Author: Nicolau Corção Saldanha

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 247

ISBN-13: 0821846280

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Presents the proceedings of the conference on Foliations, Geometry, and Topology, held August 6-10, 2007, in Rio de Janeiro, Brazil, in honor of the 70th birthday of Paul Schweitzer. The papers focus on the theory of foliations and related areas such as dynamical systems, group actions on low dimensional manifolds, and geometry of hypersurfaces.

Symplectic Topology and Measure Preserving Dynamical Systems
Symplectic Topology and Measure Preserving Dynamical Systems

Author: Albert Fathi

Publisher: American Mathematical Soc.

Published: 2010-04-09

Total Pages: 192

ISBN-13: 0821848925

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The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference on Symplectic Topology and Measure Preserving Dynamical Systems held in Snowbird, Utah in July 2007. The aim of the conference was to bring together specialists of symplectic topology and of measure preserving dynamics to try to connect these two subjects. One of the motivating conjectures at the interface of these two fields is the question of whether the group of area preserving homeomorphisms of the 2-disc is or is not simple. For diffeomorphisms it was known that the kernel of the Calabi invariant is a normal proper subgroup, so the group of area preserving diffeomorphisms is not simple. Most articles are related to understanding these and related questions in the framework of modern symplectic topology.

Spectral Analysis in Geometry and Number Theory
Spectral Analysis in Geometry and Number Theory

Author: Motoko Kotani

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 363

ISBN-13: 0821842692

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This volume is an outgrowth of an international conference in honor of Toshikazu Sunada on the occasion of his sixtieth birthday. The conference took place at Nagoya University, Japan, in 2007. Sunada's research covers a wide spectrum of spectral analysis, including interactions among geometry, number theory, dynamical systems, probability theory and mathematical physics. Readers will find papers on trace formulae, isospectral problems, zeta functions, quantum ergodicity, random waves, discrete geometric analysis, value distribution, and semiclassical analysis. This volume also contains an article that presents an overview of Sunada's work in mathematics up to the age of sixty.

Quadratic Forms -- Algebra, Arithmetic, and Geometry
Quadratic Forms -- Algebra, Arithmetic, and Geometry

Author: Ricardo Baeza

Publisher: American Mathematical Soc.

Published: 2009-08-14

Total Pages: 424

ISBN-13: 0821846485

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This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007. The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.

Differential Geometry in the Large
Differential Geometry in the Large

Author: Owen Dearricott

Publisher: Cambridge University Press

Published: 2020-10-22

Total Pages: 402

ISBN-13: 1108879993

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The 2019 'Australian-German Workshop on Differential Geometry in the Large' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kähler and Sasaki geometry.