Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1995-11-16
Phys.Rev.Lett.93:024302,2004
Nonlinear Sciences
Chaotic Dynamics
39 pages, Postscript (gzipped and uuencoded) The figures are included in low resolution only. A high resolution version can be
Scientific paper
10.1103/PhysRevLett.93.024302
The periodic orbits of the strongly chaotic cardioid billiard are studied by introducing a binary symbolic dynamics. The corresponding partition is mapped to a topological well-ordered symbol plane. In the symbol plane the pruning front is obtained from orbits running either into or through the cusp. We show that all periodic orbits correspond to maxima of the Lagrangian and give a complete list up to code length 15. The symmetry reduction is done on the level of the symbol sequences and the periodic orbits are classified using symmetry lines. We show that there exists an infinite number of families of periodic orbits accumulating in length and that all other families of geometrically short periodic orbits eventually get pruned. All these orbits are related to finite orbits starting and ending in the cusp. We obtain an analytical estimate of the Kolmogorov-Sinai entropy and find good agreement with the numerically calculated value and the one obtained by averaging periodic orbits. Furthermore the statistical properties of periodic orbits are investigated.
Bäcker Arnd
Dullin Holger R.
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