Overview
- Combines a highly readable style, clear proofs, and many examples
- Reviews essential earlier work on the discretisation of attractors and saddle points in autonomous systems
- Introduces cutting-edge work on the discretisation of attractors in nonautonomous systems
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (13 chapters)
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Dynamical Systems and Numerical Schemes
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Steady States Under Discretisation
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Autonomous Attractors Under Discretisation
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Nonautonomous Limit Sets Under Discretisation
Keywords
About this book
This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained – by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes – results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
Reviews
Authors and Affiliations
About the authors
Peter E. Kloeden completed his PhD and DSc at the University of Queensland, Australia in 1975 and 1995. He is currently a Professor of Mathematics at Huazhong University of Science & Technology in China, and an affiliated professor at Auburn University, USA. He has wide interests in the applications of mathematical analysis, numerical analysis, stochastic analysis and dynamical systems. Professor Kloeden is a co-author of several influential books on nonautonomous dynamical systems, metric spaces of fuzzy sets, and in particular “Numerical Solutions of Stochastic Differential equations” (with E. Platen) published by Springer in 1992. He is a Fellow of the Society of Industrial and Applied Mathematics and was awarded the W.T. & Idalia Reid Prize in 2006. His current interests focus on nonautonomous and random dynamical systems and their applications in the biological sciences.
Bibliographic Information
Book Title: Attractors Under Discretisation
Authors: Xiaoying Han, Peter Kloeden
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-61934-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2017
Softcover ISBN: 978-3-319-61933-0Published: 24 August 2017
eBook ISBN: 978-3-319-61934-7Published: 11 August 2017
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XI, 122
Number of Illustrations: 9 b/w illustrations, 14 illustrations in colour
Topics: Numerical Analysis, Dynamical Systems and Ergodic Theory, Ordinary Differential Equations