Computation of symbolic dynamics for one-dimensional maps |
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Authors: | Lorenzo Sella Pieter Collins |
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Affiliation: | Centrum voor Wiskunde en Informatica, Postbus 94079, 1090 GB Amsterdam, The Netherlands |
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Abstract: | In this paper we design and implement rigorous algorithms for computing symbolic dynamics for piecewise-monotone-continuous maps of the interval. The algorithms are based on computing forwards and backwards approximations of the boundary, discontinuity and critical points. We explain how to handle the discontinuities in the symbolic dynamics which occur when the computed partition element boundaries are not disjoint. The method is applied to compute the symbolic dynamics and entropy bounds for the return map of the singular limit of a switching system with hysteresis and the forced Van der Pol equation. |
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Keywords: | One-dimensional map Kneading theory Symbolic dynamics Interval arithmetic |
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