Do zeta functions for intermittent maps have branch points?

Details Do zeta functions for intermittent maps have branch points? Do zeta functions for intermittent maps have branch points?

1996-09-19

arxiv.org/abs/chao-dyn/9609012v1

Nonlinear Sciences

Chaotic Dynamics

8 pages LaTeX and 4 postscript figures using epsf.sty

Scientific paper

We present numerical evidence that the dynamical zeta function and the Fredholm determinant of intermittent maps with a neutral fix point have branch point singularities at z=1 We consider the power series expansion of zeta function and the Fredholm determinant around z=0 with the fix point pruned. This power series is computed up to order 20, requiring 10^5periodic orbits. We also discuss the relation between correlation decay and the nature of the branch point. We conclude by demonstrating how zeros of zeta functions with thermodynamic weights that are close to the branch point can be efficiently computed by a resummed cycle expansion. The idea is quite similar to that of Pade\'{e} approximants, but the ansatz is a generalized series expansion around the branch point instead of a rational function.

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