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arXiv · solv-int/9711014

Singularity confinement and chaos in discrete systems

Jarmo Hietarinta·Claude Viallet
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Abstract

We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the analysis of the complexity (``algebraic entropy'') of the map using the growth of the degree of its iterates: integrability is associated with polynomial growth while the generic growth is exponential for chaotic systems.

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Jarmo Hietarinta, Claude Viallet. 1997-11-27. Singularity confinement and chaos in discrete systems. https://doi.org/10.1103/physrevlett.81.325

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