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arXiv · 1512.09168

Singularity confinement and chaos in two-dimensional discrete systems

Masataka Kanki·Takafumi Mase·Tetsuji Tokihiro
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Abstract

We present a quasi-integrable two-dimensional lattice equation: i.e., a partial difference equation which satisfies a criterion of integrability, singularity confinement, although it has a chaotic aspect in the sense that the degrees of its iterates exhibit exponential growth. By systematic reduction to one-dimensional systems, it gives a hierarchy of ordinary difference equations with confined singularities, but with positive algebraic entropy including a generalized form of the Hietarinta-Viallet mapping. We believe that this is the first example of such quasi-integrable equations defined over a two-dimensional lattice.

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Masataka Kanki, Takafumi Mase, Tetsuji Tokihiro. 2016-04-05. Singularity confinement and chaos in two-dimensional discrete systems. https://doi.org/10.1088/1751-8113%2F49%2F23%2F23lt01

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