English

Singularity confinement and chaos in discrete systems

solv-int 2009-10-30 v1 Exactly Solvable and Integrable Systems

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.

Keywords

Cite

@article{arxiv.solv-int/9711014,
  title  = {Singularity confinement and chaos in discrete systems},
  author = {Jarmo Hietarinta and Claude Viallet},
  journal= {arXiv preprint arXiv:solv-int/9711014},
  year   = {2009}
}

Comments

4 pages, revtex, 2 PostScript-figures