publication . Other literature type . Article . 2009

Recent Development in Rigorous Computational Methods in Dynamical Systems

Arai, Zin; Kokubu, Hiroshi; Pilarczyk, Pawel;
Open Access English
  • Published: 01 Oct 2009
  • Publisher: Japan Society for Industrial and Applied Mathematics
  • Country: Brazil
Abstract
We highlight selected results of recent development in the area of rigorous computations which use interval arithmetic to analyse dynamical systems. We describe general ideas and selected details of di erent ways of approach and we provide speci c sample applications to illustrate the e ectiveness of these methods. The emphasis is put on a topological approach, which combined with rigorous calculations provides a broad range of new methods that yield mathematically reliable results. Z. Arai was partially supported by Grant-in-Aid for Scientific Research (No. 17740054).H. Kokubu was partially supported by Grant-in-Aid for Scientific Research (No. 17340045).P. Pil...
Subjects
free text keywords: Science & Technology, dynamical system, rigorous computations, algorithm, Conley index, hyperbolic dynamics, General Engineering, Applied Mathematics, Computation, Mathematical optimization, Interval arithmetic, Mathematical analysis, Dynamical systems theory, Mathematics
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publication . Other literature type . Article . 2009

Recent Development in Rigorous Computational Methods in Dynamical Systems

Arai, Zin; Kokubu, Hiroshi; Pilarczyk, Pawel;