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Attractors Under Discretisation

  • Xiaoying Han
  • Peter Kloeden

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Dynamical Systems and Numerical Schemes

    1. Front Matter
      Pages 1-1
    2. Xiaoying Han, Peter Kloeden
      Pages 3-10
    3. Xiaoying Han, Peter Kloeden
      Pages 11-31
  3. Steady States Under Discretisation

    1. Front Matter
      Pages 33-33
    2. Xiaoying Han, Peter Kloeden
      Pages 35-39
    3. Xiaoying Han, Peter Kloeden
      Pages 41-48
    4. Xiaoying Han, Peter Kloeden
      Pages 49-53
    5. Xiaoying Han, Peter Kloeden
      Pages 55-66
  4. Autonomous Attractors Under Discretisation

    1. Front Matter
      Pages 67-67
    2. Xiaoying Han, Peter Kloeden
      Pages 69-75
    3. Xiaoying Han, Peter Kloeden
      Pages 77-81
    4. Xiaoying Han, Peter Kloeden
      Pages 83-88
  5. Nonautonomous Limit Sets Under Discretisation

    1. Front Matter
      Pages 89-89
    2. Xiaoying Han, Peter Kloeden
      Pages 91-97
    3. Xiaoying Han, Peter Kloeden
      Pages 99-104
    4. Xiaoying Han, Peter Kloeden
      Pages 105-109
    5. Xiaoying Han, Peter Kloeden
      Pages 111-117
  6. Back Matter
    Pages 119-122

About this book

Introduction

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.

Keywords

One step numerical schemes Autonomous dynamicl systems Attracors and saddle points Nonautonomous attractors ODE

Authors and affiliations

  • Xiaoying Han
    • 1
  • Peter Kloeden
    • 2
  1. 1.Department of Mathematics and StatisticsAuburn UniversityAuburnUSA
  2. 2.School of Mathematics and StatisticsHuazhong University of Science and TechnologyWuhanChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-61934-7
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-61933-0
  • Online ISBN 978-3-319-61934-7
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site
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