Related papers: Dynamical zeta functions

This is a survey article on the twisted dynamical zeta functions of Ruelle and Selberg and the Fried's conjecture. It is based on the mini-course: "Twisted Ruelle zeta function, complex-valued analytic torsion and the Fried's conjecture",…

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…

We study the Ruelle dynamical determinant of a real analytic diffeomorphism on a compact surface, assuming that the tangent space over the nonwandering set admits a dominated splitting. Combining previous work of Pujals and Sambarino with…

Transfer operators M_k acting on k-forms in R^n are associated to smooth transversal local diffeomorphisms and compactly supported weight functions. A formal trace is defined by summing the product of the weight and the Lefschetz sign over…

We generalise Milnor-Thurston's kneading theory to the setting of piecewise continuous and monotone interval maps with weights. We define a weighted kneading determinant ${\cal D}(t)$ and establish combinatorially two kneading identities,…

We consider the dynamical zeta functions of Selberg and Ruelle associated with the geodesic flow on a compact odd-dimensional hyperbolic manifold. These dynamical zeta functions are defined for a complex variable $s$ in some right-half…

We construct a version of kneading theory for families of monotonous functions on the real line. The generality of the setup covers two classical results from Milnor-Thurston's kneading theory: the first one is to dynamically characterise…

A dynamical zeta function $\zeta$ and a transfer operator $\scr L$ are associated with a piecewise monotone map $f$ of the interval $[0,1]$ and a weight function $g$. The analytic properties of $\zeta$ and the spectral properties of $\scr…

For smooth hyperbolic dynamical systems and smooth weights, we relate Ruelle transfer operators with dynamical Fredholm determinants and dynamical zeta functions: First, we establish bounds for the essential spectral radii of the transfer…

We present a numerical algorithm for the computation of invariant Ruelle distributions on convex co-compact hyperbolic surfaces. This is achieved by exploiting the connection between invariant Ruelle distributions and residues of…

We introduce a Milnor metric on the determinant line of the cohomology of the underlying closed manifold with coefficients in a flat vector bundle, by means of interactions between the fixed points and the closed orbits of a Morse-Smale…

We prove a regularized determinant formula for the zeta functions of certain 3-dimensional Riemannian foliated dynamical systems, in terms of the infinitesimal operator induced by the flow acting on the reduced leafwise cohomologies. It is…

In recent years Lichtenbaum has conjectured a description for the special values of Hasse--Weil zeta functions in terms of ``Weil-\'etale cohomology''. In earlier papers we studied a class of foliated dynamical systems which had some…

In this brief note we present a very simple strategy to investigate dynamical determinants for uniformly hyperbolic systems. The construction builds on the recent introduction of suitable functional spaces which allow to transform simple…

Summations and relations involving the Hurwitz and Riemann zeta-functions are extended first to Barnes zeta-functions and then to zeta-functions of general type. The analysis is motivated by the evaluation of determinants on spheres which…

These notes are based on three lectures given by the second author at Copenhagen University (October 2009) and at Aarhus University, Denmark (December 2009). We mostly present here a survey of results of Dieter Mayer on relations between…

We derive simple new expressions, in various dimensions, for the functional determinant of a radially separable partial differential operator, thereby generalizing the one-dimensional result of Gel'fand and Yaglom to higher dimensions. We…

This article introduces and investigates the basic features of a dynamical zeta function for group actions, motivated by the classical dynamical zeta function of a single transformation. A product formula for the dynamical zeta function is…

We describe a general method to prove meromorphic continuation of dynamical zeta functions to the entire complex plane under the condition that the corresponding partition functions are given via a dynamical trace formula from a family of…

In this paper, we consider the dynamical zeta functions of Ruelle and Selberg associated with the geodesic flow of a compact hyperbolic odd dimensional manifold $X$. These functions are initially defined on one complex variable $s$ in some…