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Recent development in rigorous computational methods in dynamical systems

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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.

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Author information

Authors and Affiliations

  1. Creative Research Institution “Sousei”, Hokkaido University, N21W10 Kita-ku, 001-0021, Sapporo, Japan

    Zin Arai

  2. PRESTO, Japan Science and Technology Agency, Japan

    Zin Arai

  3. Department of Mathematics, Kyoto University, 606-8502, Kyoto, Japan

    Hiroshi Kokubu

  4. Centre of Mathematics Campus de Gualtar, University of Minho, 4710-057, Braga, Portugal

    Paweł Pilarczyk

Authors
  1. Zin Arai
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  2. Hiroshi Kokubu
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  3. Paweł Pilarczyk
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Additional information

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. Pilarczyk was partially supported by the JSPS Postdoctoral Fellowship (No. P06039) at the Department of Mathematics, Kyoto University, and by Grant-in-Aid for Scientific Research (No. 1806039).

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Arai, Z., Kokubu, H. & Pilarczyk, P. Recent development in rigorous computational methods in dynamical systems. Japan J. Indust. Appl. Math. 26, 393–417 (2009). https://doi.org/10.1007/BF03186541

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  • DOI: https://doi.org/10.1007/BF03186541

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