Differential Equations And Dynamical Systems: 2 Usuzcamp, Urgench, Uzbekistan, August 8–12, 2017

Springer Proceedings in Mathematics & Statistics Abdulla Azamov Leonid Bunimovich Akhtam Dzhalilov Hong-Kun Zhang Editors Differential Equations and Dynamical Systems 2 USUZCAMP, Urgench, Uzbekistan, August 8–12, 2017 Springer Proceedings in Mathematics & Statistics Volume 268 Springer Proceedings in Mathematics & Statistics This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics, including operation research and optimization. In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematical and statistical research today. More information about this series at http://www.springer.com/series/10533 Abdulla Azamov Leonid Bunimovich Akhtam Dzhalilov Hong-Kun Zhang • • Editors Differential Equations and Dynamical Systems 2 USUZCAMP, Urgench, Uzbekistan, August 8–12, 2017 123 Editors Abdulla Azamov Institute of Mathematics Uzbekistan Academy of Sciences Tashkent, Uzbekistan Leonid Bunimovich School of Mathematics Georgia Institute of Technology Atlanta, GA, USA Akhtam Dzhalilov Turin Polytechnic University Tashkent, Uzbekistan Hong-Kun Zhang Department of Mathematics and Statistics University of Massachusetts Amherst Amherst, MA, USA ISSN 2194-1009 ISSN 2194-1017 (electronic) Springer Proceedings in Mathematics & Statistics ISBN 978-3-030-01475-9 ISBN 978-3-030-01476-6 (eBook) https://doi.org/10.1007/978-3-030-01476-6 Library of Congress Control Number: 2018955929 Mathematics Subject Classification (2010): 37E10, 26A18, 28D05, 34C05, 34C28, 34D05, 34D45, 37C55, 37A05, 37A60, 37A50, 37D50, 37D25 © Springer Nature Switzerland AG 2018 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 Contents On Linearization of Circle Diffeomorphisms . . . . . . . . . . . . . . . . . . . . . Akhadkulov Habibulla, Dzhalilov Akhtam and Konstantin Khanin 1 The Fujita and Secondary Type Critical Exponents in Nonlinear Parabolic Equations and Systems . . . . . . . . . . . . . . . . . . . Aripov Mersaid 9 A Language of Terms of Taylor’s Formula for Quadratic Dynamical Systems and