Billiard Sequences and the Property of Splittability of Integrable Hamilton Systems

Details Billiard Sequences and the Property of Splittability of Integrable Hamilton Systems Billiard Sequences and the Property of Splittability of Integrable Hamilton Systems

1999-11-16

arxiv.org/abs/chao-dyn/9911020v1

Nonlinear Sciences

Chaotic Dynamics

9 pages, Latex

Scientific paper

The paper establishes the property of splittability of billiard boundary sequences in n dimensional cube into subsequences of fractional parts. This reveals a new property of integrable and weak perturbated Hamilton systems: under a simple assumption, the boundary motion of elliptic orbits on stable KAM tori, if considering in cartesian coordinates, can be splitted into a countable set of discrete rotations. The rate of the split process, expressed in terms of some exceptional sets density, in dependence of number-theoretical characteristics of the orbits frequencies, is also examined.

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