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Attractors Under Discretisation

SpringerBriefs in Mathematics

Format: Paperback / softback
Publisher: Springer International Publishing AG, Cham, Switzerland
Published: 24th Aug 2017
Dimensions: w 156mm h 234mm d 7mm
Weight: 202g
ISBN-10: 3319619330
ISBN-13: 9783319619330
Barcode No: 9783319619330
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Synopsis
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.

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"The book is based on lecture notes while the material is based on papers, partially by the authors. ... But the lecture style is quite accessible and the book has a logical structure with theorems and proofs, and clear examples. The proofs are polished and the text reads easily. A target audience would be advanced students and researchers in dynamical systems with a more theoretical focus, in which the lecturers could provide any missing details." (Hil G. E. Meijer, Mathematical reviews, September, 2018)