Mark Pollicott's Books

Dynamical Systems and Ergodic Theory

By: Mark Pollicott,Michiko Yuri

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Dynamical Systems and Ergodic Theory

By: Mark Pollicott,Michiko Yuri

This book is an essentially self contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a masters level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der waerden's theorem and szemerdi's theorem).

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Page Count

198

Publisher

Cambridge University Press

Published Date

ISBN 10

0521575990

ISBN 13

9780521575997

Open Conformal Systems and Perturbations of Transfer Operators

By: Mark Pollicott,Mariusz Urbański

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Open Conformal Systems and Perturbations of Transfer Operators

By: Mark Pollicott,Mariusz Urbański

The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic conformal systems this has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved. The asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet iterated function systems. These results have direct applications to interval maps, rational functions and meromorphic maps. Towards this goal the authors develop, on a purely symbolic level, a theory of singular perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet subshifts of finite type and Hölder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets.

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Page Count

207

Publisher

Springer

Published Date

ISBN 10

3319721798

ISBN 13

9783319721798

Asymptotic Counting in Conformal Dynamical Systems

By: Mark Pollicott,Mariusz Urba?ski

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Asymptotic Counting in Conformal Dynamical Systems

By: Mark Pollicott,Mariusz Urba?ski

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Page Count

139

Publisher

American Mathematical Society

Published Date

ISBN 10

1470465779

ISBN 13

9781470465773

Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds

By: Mark Pollicott

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Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds

By: Mark Pollicott

These lecture notes provide a unique introduction to Pesin theory and its applications.

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Page Count

176

Publisher

Cambridge University Press

Published Date

ISBN 10

0521435935

ISBN 13

9780521435932

Extremes and Recurrence in Dynamical Systems

By: Valerio Lucarini,Davide Faranda,Ana Cristina Gomes Monteiro Moreira de Freitas,Jorge Miguel Milhazes de Freitas,Mark Holland,Tobias Kuna,Matthew Nicol,Mike Todd,Sandro Vaienti

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Extremes and Recurrence in Dynamical Systems

By: Valerio Lucarini,Davide Faranda,Ana Cristina Gomes Monteiro Moreira de Freitas,Jorge Miguel Milhazes de Freitas,Mark Holland,Tobias Kuna,Matthew Nicol,Mike Todd,Sandro Vaienti

Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.

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Page Count

325

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118632192

ISBN 13

9781118632192

Dynamical Systems and Ergodic Theory

By: Mark Pollicott,Michiko Yuri

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Dynamical Systems and Ergodic Theory

By: Mark Pollicott,Michiko Yuri

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Page Count

198

Publisher

Cambridge University Press

Published Date

ISBN 10

0521575990

ISBN 13

9780521575997

Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds

By: Mark Pollicott

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Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds

By: Mark Pollicott

These lecture notes provide a unique introduction to Pesin theory and its applications.

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Page Count

176

Publisher

Cambridge University Press

Published Date

ISBN 10

0521435935

ISBN 13

9780521435932

Asymptotic Counting in Conformal Dynamical Systems

By: Mark Pollicott,Mariusz Urba?ski

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Asymptotic Counting in Conformal Dynamical Systems

By: Mark Pollicott,Mariusz Urba?ski

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Page Count

139

Publisher

American Mathematical Society

Published Date

ISBN 10

1470465779

ISBN 13

9781470465773

Open Conformal Systems and Perturbations of Transfer Operators

By: Mark Pollicott,Mariusz Urbański

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Open Conformal Systems and Perturbations of Transfer Operators

By: Mark Pollicott,Mariusz Urbański

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Page Count

207

Publisher

Springer

Published Date

ISBN 10

3319721798

ISBN 13

9783319721798

Equilibrium States in Negative Curvature

By: Barbara Schapira

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Equilibrium States in Negative Curvature

By: Barbara Schapira

With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities) allowing us to get rid of compactness assumptions on the manifold, and prove many existence, uniqueness and finiteness results of Gibbs measures. We give many applications to the variational principle, the counting and equidistribution of orbit points and periods, the unique ergodicity of the strong unstable foliation and the classification of Gibbs densities on some Riemannian covers

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Page Count

281

Published Date

ISBN 10

2856298184

ISBN 13

9782856298183

Book's by Mark Pollicott

Dynamical Systems and Ergodic Theory

Dynamical Systems and Ergodic Theory

Open Conformal Systems and Perturbations of Transfer Operators

Open Conformal Systems and Perturbations of Transfer Operators

Asymptotic Counting in Conformal Dynamical Systems

Asymptotic Counting in Conformal Dynamical Systems

Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds

Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds

Extremes and Recurrence in Dynamical Systems

Extremes and Recurrence in Dynamical Systems

Dynamical Systems and Ergodic Theory

Dynamical Systems and Ergodic Theory

Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds

Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds

Asymptotic Counting in Conformal Dynamical Systems

Asymptotic Counting in Conformal Dynamical Systems

Open Conformal Systems and Perturbations of Transfer Operators

Open Conformal Systems and Perturbations of Transfer Operators

Equilibrium States in Negative Curvature

Equilibrium States in Negative Curvature

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