Qualitative Analysis of Set-Valued Differential Equations
The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for
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Qualitative Analysis of Set-Valued Differential Equations
Anatoly A. Martynyuk
Qualitative Analysis of Set-Valued Differential Equations
Anatoly A. Martynyuk Institute of Mechanics National Academy of Sciences of Ukraine Kiev, Ukraine
ISBN 978-3-030-07643-6 ISBN 978-3-030-07644-3 (eBook) https://doi.org/10.1007/978-3-030-07644-3 Library of Congress Control Number: 2018968441 Mathematics Subject Classification (2010): 34A34, 34A37, 34A60, 49J24, 49K24, 34D20, 34D40, 34G99, 93B12, 93B27, 93C41, 93D09, 93D30 © 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 book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Simplicity is the only soil on which we can erect the building of our generalizations. A. Poincaré
Preface
The construction of the theory of dynamic system trajectories is rooted in the classical works by Poincare and Lyapunov. The notion of phase space introduced by Gibbs allows one to consider the motion of a mechanical system as the motion of an image point in some n-dimensional space of configurations or, what is the same, in the phase space with given metric. Darboux treated a dynamical system as a point moving in n-dimensional space. This idea was successively applied in the papers by Hertz, where the trajectories were considered as the geodesic lines. In the papers by Painleve, the trajectories of mechanical systems were studied in the context of the ideas of multidimensional geometry with the use of Euclidean metric. The ideas of multidimensional geometry were extensively applied in the investigation of the trajectories of mechanical systems in the works by Ricci and Levi-Civita, Sing, and Belenkiy and many others. The recent studies of complex
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