Japan Journal of Industrial and Applied Mathematics

Recent Development in Rigorous Computational Methods in Dynamical Systems

Zin Arai, Hiroshi Kokubu, and Paweł Pilarczyk

Full-text: Open access

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 different ways of approach and we provide specific sample applications to illustrate the effectiveness 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.

Article information

Source
Japan J. Indust. Appl. Math. Volume 26, Number 2-3 (2009), 393-417.

Dates
First available in Project Euclid: 1 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.jjiam/1265033788

Mathematical Reviews number (MathSciNet)
MR2589482

Zentralblatt MATH identifier
1184.65117

Keywords
dynamical system rigorous computations algorithm Conley index hyperbolic dynamics

Citation

Arai, Zin; Kokubu, Hiroshi; Pilarczyk, Paweł. Recent Development in Rigorous Computational Methods in Dynamical Systems. Japan J. Indust. Appl. Math. 26 (2009), no. 2-3, 393--417. https://projecteuclid.org/euclid.jjiam/1265033788.


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