New Advances on Chaotic Intermittency and its Applications
One of the most important routes to chaos is the chaotic intermittency. However, there are many cases that do not agree with the classical theoretical predictions. In this book, an extended theory for intermittency in one-dimensional maps is presented. A
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New Advances on Chaotic Intermittency and its Applications
New Advances on Chaotic Intermittency and its Applications
Sergio Elaskar • Ezequiel del Río
New Advances on Chaotic Intermittency and its Applications
123
Ezequiel del Río Polytechnic University of Madrid Madrid, Madrid, Spain
Sergio Elaskar National University of Cordoba Ciudad de Córdoba Córdoba, Argentina
ISBN 978-3-319-47836-4 DOI 10.1007/978-3-319-47837-1
ISBN 978-3-319-47837-1 (eBook)
Library of Congress Control Number: 2016955367 © Springer International Publishing AG 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. 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
To my wife, Mila, and my daughter, Alba (EdR)
To my family, María Inés, Silvina and Daniel (SE)
Preface
From the pioneer works of H. Poincaré to present days, the nonlinear science has developed tremendously. In particular, chaos theory presents nowadays a number of fields of investigation. One of such fields is the so-called routes to chaos, where an interesting one is the chaotic intermittency, because this phenomenon has been observed in many different fields. The intermittency theory coming from the early 1980s was based on a strong hypothesis on the reinjection probability density function (RPD). From early times, “pathology cases” were found, that is, systems showing chaotic intermittency with statistic properties not fully explained basing on the classical theory. These cases demand a broader intermittency theory looking for a new and more general RPD function. By means of the Poincaré map, many continuous systems can be investigated by one-dimensional maps. In this book, new methodologies to investigate chaotic intermittency in one-dimensional maps are presented. A new general methodology to evaluate the RPD is developed. The core of this formulation is
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