Dynamical zeta functions for tree maps
نویسنده
چکیده
We study piecewise monotone and piecewise continuous maps f from a rooted oriented tree to itself, with weight functions either piecewise constant or of bounded variation. We deene kneading coordinates for such tree maps. We show that the Milnor-Thurston relation holds between the weighted reduced zeta function and the weighted kneading determinant of f. This generalizes a result known for piecewise monotone interval maps.
منابع مشابه
Do zeta functions for intermittent maps have branch points ?
We present numerical evidence that the dynamical zeta function ζ(z) and the Fredholm determinant F (z) of intermittent maps with a neutral fix point have branch point singularities at z = 1. We consider the power series expansion of 1/ζ(z) and F (z) around z = 0 with the fix point pruned. This power series is computed up to order 20, requiring ∼ 10 5 periodic orbits. We also discuss the relatio...
متن کاملFractal diffusion coefficient from dynamical zeta functions
Abstract. Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of the grammar rules that may lead to a non smooth dependence of global observable on parameters changes. A paradigmatic example is the fractal diffusio...
متن کاملOn the effect of pruning on the singularity structure of zeta functions
We investigate the topological zeta function for unimodal maps in general and dynamical zeta functions for the tent map in particular. For the generic situation, when the kneading sequence is aperiodic, it is shown that the zeta functions have a natural boundary along its radius of convergence, beyond which the function lacks analytic continuation. We make a detailed study of the function ∏∞ n=...
متن کاملPeriodic Orbits and Zeta Functions
0. Introduction 1 1. Twisted orbits and zeta functions 3 2. Axiom A diieomorphisms 4 3. Symbolic dynamics and rationality 5 4. Zeta functions and for interval maps 9 5. The Ruelle zeta function 14 6. Zeta functions for hyperbolic ows 21 7. Zeta functions for analytic Anosov ows 25 8. L-functions and special values 26 9. counting closed orbits for ows 27 10. L-functions and homology 32 11. Pole ...
متن کاملA New Determinant for Quantum Chaos
Dynamical zeta functions [1], Fredholm determinants [2] and quantum Selberg zeta functions [3, 4] have recently been established as powerful tools for evaluation of classical and quantum averages in low dimensional chaotic dynamical systems [5] [8]. The convergence of cycle expansions [9] of zeta functions and Fredholm determinants depends on their analytic properties; particularly strong resul...
متن کامل