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. Aimed at the graduate/upper undergraduate level, the emphasis is on dynamical systems with discrete
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Luís Barreira Claudia Valls
Dynamical Systems by Example
Problem Books in Mathematics Series Editor Peter Winkler Department of Mathematics Dartmouth College Hanover, NH USA
More information about this series at http://www.springer.com/series/714
Luís Barreira Claudia Valls •
Dynamical Systems by Example
123
Luís Barreira Instituto Superior Técnico Universidade de Lisboa Lisbon, Portugal
Claudia Valls Instituto Superior Técnico Universidade de Lisboa Lisbon, Portugal
ISSN 0941-3502 ISSN 2197-8506 (electronic) Problem Books in Mathematics ISBN 978-3-030-15914-6 ISBN 978-3-030-15915-3 (eBook) https://doi.org/10.1007/978-3-030-15915-3 Library of Congress Control Number: 2019934778 Mathematics Subject Classification (2010): 37-01, 37Dxx, 37Bxx, 37Exx, 37Axx © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This book is a large collection of problems, all with detailed solutions, on the core of the theory of dynamical systems. Besides the basic theory, the topics include topological dynamics, low-dimensional dynamics, hyperbolic dynamics, symbolic dynamics, and basic ergodic theory. As in any other area of mathematics, it is important while learning dynamical systems to solve selected problems (always after a careful study of the material!), in particular to get a first working knowledge of the topics as well as of some less direct difficulties. It goes without saying that this helped substantially generations of mathematicians in getting a solid understanding of the theory and of its applications. Nevertheless, it is difficult to find large collections of problems on less basic subjects, at least other than on quite specific topics. Moreover, these
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