Abstract We show continuity under equivariant Gromov–Hausdorff convergence of the critical exponent discrete, non-elementary, torsion-free, quasiconvex-cocompact groups with uniformly bounded codiameter acting on Gromov-hyperbolic metric spaces.

We study the spectrum of transfer operators associated to various dynamical systems. Our aim is obtain precise information on discrete spectrum. To this end we propose a unitary approach. consider settings where new can be obtained following different branches along proposed path. These include affine expanding Markov maps, uniformly non-uniformly or simply monotone hyperbolic diffeomorphisms. ...

Hyperbolic systems of dissipative type, contracting the phase space volume, manifest robust attractors. There are several classes of discrete time systems which produce hyperbolic nontrivial attractor – like the Plykin attractors [P] or the Smale attractors [KH]. Recently, Kuznetsov [K] proposed a continuous model for which there is a good numerical evidence of the existence of an uniformly hyp...

Using a special form of Ulam’s method, we estimate the measure-theoretic entropy of a triple (M, T , μ), where M is a smooth manifold, T is a C1+γ uniformly hyperbolic map, and μ is the unique physical measure of T . With a few additional calculations, we also obtain numerical estimates of (i) the physical measureμ, (ii) the Lyapunov exponents of T with respect toμ, (iii) the rate of decay of c...

Using an approach due to Bowen, Franco showed that continuous expansive flows with specification have unique equilibrium states for potentials with the Bowen property. We show that this conclusion remains true using weaker non-uniform versions of specification, expansivity, and the Bowen property. We also establish a corresponding result for homeomorphisms. In the homeomorphism case, we obtain ...

Let f : M → M be a C-map on a smooth Riemannian manifold M and let Λ ⊂ M be a compact f -invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of f |Λ. These results are non-invertible and, in particular, non-uniformly hyperbolic versions of well-known results by Bowen, Ruelle, and others in the case of hyperbolic diffeomorphis...

We prove a generalization of the fellow traveller property for certain type quasi-geodesics and use it to present three equivalent geometric formulations bounded reduction that this is preservation coarse median. then provide an affirmative answer question from Araújo Silva as whether every nontrivial uniformly continuous endomorphism hyperbolic group with respect visual metric satisfies Hölder...

We construct SRB measures for endomorphisms satisfying conditions far weaker than the usual non-uniform expansion. As a consequence, the definition of a non-uniformly expanding map can be weakened. We also prove the existence of an absolutely continuous invariant measure for local diffeomorphisms, only assuming the existence of hyperbolic times for Lebesgue almost every point in the manifold.