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Attractors Under Discretisation
Englisch
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This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. Key results for autonomous ODEs were obtained in the1980s by Beyn for saddle points and 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. A main aim of this book is to present new results on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, in particular work on the properties of nonautonomous omega limit sets and their approximations by numerical schemes. These results are also of interest for autonomous systems which are approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
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