Singularity confinement and chaos in discrete systems

Details Singularity confinement and chaos in discrete systems Singularity confinement and chaos in discrete systems

1997-11-27

arxiv.org/abs/solv-int/9711014v1

Phys. Rev. Lett., 81 (1998) 325

Nonlinear Sciences

Exactly Solvable and Integrable Systems

4 pages, revtex, 2 PostScript-figures

Scientific paper

10.1103/PhysRevLett.81.325

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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