The Space of Dynamical Systems with the C0-Topology
This book is an introduction to main methods and principal results in the theory of Co(remark: o is upper index!!)-small perturbations of dynamical systems. It is the first comprehensive treatment of this topic. In particular, Co(upper index!)-generic pro
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Lecture Notes in Mathematics Editors: A. Dold, Heidelberg B. Eckmann, Zurich F. Takens, Groningen
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Sergei Yu. Pilyugin
The Space of Dynamical Systems with the CO-Topology
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Author Sergei Yu. Pilyugin Department of Mathematics and Mechanics St. Petersburg State University Bibliotechnaya pI. 2, Petrodvorets 198904 St. Petersburg, Russia
Mathematics Subject Classification (1991): 58F30, 58FIO, 58F12, 58F40, 54H20, 65L99
ISBN 3-540-57702-5 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-57702-5 Springer-Verlag New York Berlin Heidelberg
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46/3140-543210 - Printed on acid-free paper
Preface A standard object of interest in the global qualitative theory of dynamical systems is the space of smooth dynamical systems with the C1-topology. In recent years many deep and important results were obtained in the theory of structural stability. These results are mostly based on the following fundamental fact : we may consider a C1-small perturbation of a smooth dynamical system as a perturbation in a neighborhood of any trajectory which does not change essentially the corresponding "first approximation" linear system. It is known for a long time (beginning with works of A.Lyapunov and H.Poincare) that under some intrinsic conditions on the "first approximation" system perturbations of this sort do not change the local structure of a neighborhood of a trajectory. The situation becomes quite different if we study CD-small perturbations of a system. It is easy to understand that arbitrarily CD-small perturbation can result in a complete change of the qualitative behaviour of trajectories in a neighborhood of a fixed trajectory. Nevertheless the theory of CD-small perturbations of dynamical systems which was developed intensively over the last 20 years contains now many interesting results. It was an intention of the author to give the reader an initial perspective of the theory. So we are going to give in this book an introduction to some of the main methods of the theory and to formulate its principal results. Of course, this book is a reflection of scientific interests of the author, hence we pay more attention to problems which are close to the author's own works. This book is an introduction rather than a monograph. That's why the author tried to simplify an
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