Weyl law for open systems with sharply divided mixed phase space

Details Weyl law for open systems with sharply divided mixed phase space Weyl law for open systems with sharply divided mixed phase space

2012-03-20

arxiv.org/abs/1203.4462v2

Nonlinear Sciences

Chaotic Dynamics

8 pages, 14 figures

Scientific paper

10.1103/PhysRevE.85.046203

A generalization of the Weyl law to systems with a sharply divided mixed phase space is proposed. The ansatz is composed of the usual Weyl term which counts the number of states in regular islands and a term associated with sticky regions in phase space. For a piecewise linear map, we numerically check the validity of our hypothesis, and find good agreement not only for the case with a sharply divided phase space, but also for the case where tiny island chains surround the main regular island. For the latter case, a non-trivial power law exponent appears in the survival probability of classical escaping orbits, which may provide a clue to develop the Weyl law for more generic mixed systems.

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