Chaos An Introduction for Applied Mathematicians
This is a textbook on chaos and nonlinear dynamics, written by applied mathematicians for applied mathematicians. It aims to tread a middle ground between the mathematician's rigour and the physicist’s pragmatism. While the subject matter is now clas
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Chaos An Introduction for Applied Mathematicians
Chaos
Andrew Fowler Mark McGuinness •
Chaos An Introduction for Applied Mathematicians
123
Andrew Fowler MACSI University of Limerick Limerick, Ireland
Mark McGuinness School of Mathematics and Statistics Victoria University of Wellington Wellington, New Zealand
ISBN 978-3-030-32537-4 ISBN 978-3-030-32538-1 https://doi.org/10.1007/978-3-030-32538-1
(eBook)
Mathematics Subject Classification (2010): 34A34, 34C23, 34C28, 34C37, 37B10, 37C29, 37D45, 37E05, 37J40 © 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, expressed 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. Front cover image: a drawing of water pouring into a pool by Leonardo da Vinci, ca. 1507. Windsor Collection 12660v. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
We dedicate this book to Stephen O’Brien, who has variously brought both chaos and order, in differing measures, to each of us. Stephen is a leader in applied mathematics in Ireland at the present time, and is a figurehead in the effort to bring the subject there to a level where it seriously engages with industry, science and nature. Under his leadership, the Mathematics Applications Consortium for Science and Industry (MACSI) at the University of Limerick has become a flagship for applied mathematics in Ireland.
Preface
The modern theory of chaos arguably stems from the publication of Ed Lorenz’s remarkable paper in 1963 on deterministic nonperiodic flow. It took a while for it to be noticed outside the meteorological literature, but by the 1970s, the subject was gaining momentum, courses were created and in the 1980s books started to appear. At first few in number, but eventually they too became a roaring current. The subject is now well established, and as well as plentiful li
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