Zbigniew Galias 2002 Nonlinearity 15 1759 doi:10.1088/0951-7715/15/6/304
Rigorous investigation of the Ikeda map by means of interval arithmetic
Zbigniew Galias
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In this work we present various tools for studying dynamical systems implemented in interval arithmetic. The methods include an algorithm for finding all low-period cycles enclosed in a specified region, finding an upper bound of the invariant and nonwandering part of a given set, finding a lower bound of the basin of attraction of a stable periodic orbit, and proving the existence of symbolic dynamics of a given type embedded in the map. Using these techniques a detailed study of the behaviour of the Ikeda map for different parameter values is performed.
- PACS
- MSC
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37C25 Fixed points, periodic points, fixed-point index theory
- Subjects
- Dates
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Issue 6 (November 2002)
Received 28 August 2001, in final form 2 August 2002
Published 16 September 2002
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Rigorous investigation of the Ikeda map by means of interval arithmetic
Zbigniew Galias 2002 Nonlinearity 15 1759
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