Ergodic Optimization in the Expanding Case Concepts, Tools and Appli
This book focuses on the interpretation of ergodic optimal problems as questions of variational dynamics, employing a comparable approach to that of the Aubry-Mather theory for Lagrangian systems. Ergodic optimization is primarily concerned with the study
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Eduardo Garibaldi
Ergodic Optimization in the Expanding Case Concepts, Tools and Applications 123
SpringerBriefs in Mathematics Series Editors Nicola Bellomo Michele Benzi Palle Jorgensen Tatsien Li Roderick Melnik Otmar Scherzer Benjamin Steinberg Lothar Reichel Yuri Tschinkel George Yin Ping Zhang
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Eduardo Garibaldi
Ergodic Optimization in the Expanding Case Concepts, Tools and Applications
123
Eduardo Garibaldi University of Campinas - IMECC Campinas, São Paulo, Brazil
ISSN 2191-8198 ISSN 2191-8201 (electronic) SpringerBriefs in Mathematics ISBN 978-3-319-66642-6 ISBN 978-3-319-66643-3 (eBook) DOI 10.1007/978-3-319-66643-3 Library of Congress Control Number: 2017954979 © The Author(s) 2017 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
These notes grew out of a graduate course on ergodic optimization given by the author at the University of Campinas. Obviously, some background in ergodic theory is required to follow the text. The requisites are relatively light: a reader should be familiar with the basic concepts of ergodic theory, as contained in, for example, the first half of Walters’ book [101]. Moreover, these notes are by no means meant to be exhaustive. As a matter
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