Dynamical zeta functions for Artin's billiard and the Venkov--Zograf factorization formula

Details Dynamical zeta functions for Artin's billiard and the Venkov--Zograf factorization formula Dynamical zeta functions for Artin's billiard and the Venkov--Zograf factorization formula

1993-07-02

arxiv.org/abs/chao-dyn/9307001v1

Nonlinear Sciences

Chaotic Dynamics

18 pages, no figures

Scientific paper

10.1016/0167-2789(94)90070-1

Dynamical zeta functions are expected to relate the Schr\"odinger operator's spectrum to the periodic orbits of the corresponding fully chaotic Hamiltonian system. The relationsship is exact in the case of surfaces of constant negative curvature. The recently found factorisation of the Selberg zeta function for the modular surface is known to correspond to a decomposition of the Schr\"odinger operator's eigenfunctions into two sets obeying different boundary condition on Artin's billiard. Here we express zeta functions for Artin's billiard in terms of generalized transfer operators, providing thereby a new dynamical proof of the above interpretation of the factorization formula. This dynamical proof is then extended to the Artin--Venkov--Zograf formula for finite coverings of the modular surface.

Affiliated with

Also associated with

No associations

Rating

Dynamical zeta functions for Artin's billiard and the Venkov--Zograf factorization formula does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dynamical zeta functions for Artin's billiard and the Venkov--Zograf factorization formula, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamical zeta functions for Artin's billiard and the Venkov--Zograf factorization formula will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-488465