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Zeta functions and the periodic orbit structure of hyperbolic dynamics
© Société mathématique de France, 1990, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les
Equilibrium States in Negative Curvature
With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework
On introduit une classe de flots plus generaux que les flots de l'axiome A et on montre que certains resultats pour ces derniers restent vrais
Multifractal Analysis of Lyapunov Exponent for Continued Fraction and Manneville–Pomeau Transformations and Applications to Diophantine Approximation
Abstract:We extend some of the theory of multifractal analysis for conformal expanding systems to two new cases: The non-uniformly hyperbolic example of the Manneville–Pomeau equation and the
An analogue of the prime number theorem for closed orbits of Axiom A flows
For an Axiom A flow restricted to a basic set we extend the zeta function to an open set containing W(s) > h where h is the topological entropy. This enables us to give an asymptotic formula for the
Meromorphic extensions of generalised zeta functions
SummaryIn this paper we give a full description of the spectrum of the Ruelle-Perron-Frobenius operator acting on the Banach space of Holder continuous functions on a subshift of finite type (Theorem
Anosov flows and dynamical zeta functions
We study the Ruelle and Selberg zeta functions for C r Anosov ows, r > 2, on a compact smooth manifold. We prove several results, the most remarkable being (a) for C 1 ows the zeta function is
Exponential error terms for growth functions on negatively curved surfaces
<abstract abstract-type="TeX"><p>In this paper we consider two counting problems associated with compact negatively curved surfaces and improve classical asymptotic estimates due to Margulis. In the
The Hausdorff dimension of -expansions with deleted digits
A process and apparatus for the gaseous reduction of sized iron ores wherein a steam-hydrocarbon fluid mixture, having a steam : carbon molar ratio ranging from 0.9:1 to 1.8:1, is catalytically