Multiplicities of Periodic Orbit Lengths for Non-Arithmetic Models

Details Multiplicities of Periodic Orbit Lengths for Non-Arithmetic Models Multiplicities of Periodic Orbit Lengths for Non-Arithmetic Models

2003-12-22

arxiv.org/abs/nlin/0312057v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1088/0305-4470/37/16/003

Multiplicities of periodic orbit lengths for non-arithmetic Hecke triangle groups are discussed. It is demonstrated both numerically and analytically that at least for certain groups the mean multiplicity of periodic orbits with exactly the same length increases exponentially with the length. The main ingredient used is the construction of joint distribution of periodic orbits when group matrices are transformed by field isomorphisms. The method can be generalized to other groups for which traces of group matrices are integers of an algebraic field of finite degree.

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