Related papers: Conformal measures for meromorphic maps

Let f(z)=z^2+c be an infinitely renormalizable quadratic polynomial and J_\infty be the intersection of forward orbits of "small" Julia sets of its simple renormalizations. We prove that if f admits an infinite sequence of satellite…

For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials h the topological pressure is entirely determined by the values of h on the repelling periodic points of f. This is a…

Let $\mathcal F$ be a holomorphic foliation on a compact K\'ahler surface with hyperbolic singularities and no foliation cycle. We prove that if the limit set of $\mathcal F$ has zero Lebesgue measure, then its complement is a modification…

We use Bowen's definition of topological entropy and Ahlfors five islands theorem, as well as the theory of polynomial-like mappings, to show that the topological entropy of any entire transcendental function is infinity. In addition the…

The escaping set I(f) of a transcendental meromorphic function f consists of all points which tend to infinity under iteration. The Eremenko-Lyubich class B consists of all transcendental meromorphic functions for which the set of finite…

We extend the definition of topological pressure to locally compact Hausdorff spaces, and we demonstrate a "variational principle" comparing the topological and measure theoretic pressures. Given a continuous $\mathbb{Z}_+^N$-action $T$…

We study the measure theoretic properties of typical C 0 maps of the interval. We prove that any ergodic measure is pseudo-physical, and conversely, any pseudo-physical measure is in the closure of the ergodic measures, as well as in the…

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium…

We prove that every hyperbolic measure invariant under a C^{1+\alpha} diffeomorphism of a smooth Riemannian manifold possesses asymptotically ``almost'' local product structure, i.e., its density can be approximated by the product of the…

Let $f$ be a meromorphic correspondence on a compact K\"ahler manifold $X$ of dimension $k$. Assume that its topological degree is larger than the dynamical degree of order $k-1$. We obtain a quantitative regularity of the equilibrium…

Let $(X, g^+)$ be an asymptotically hyperbolic manifold and $(M, [\hat{h}])$ its conformal infinity. Our primary aim in this paper is to introduce the prescribed fractional scalar curvature problem on $M$ and provide solutions under various…

We introduce the {\em $\mu$-topological stability}. This is a type of stability depending on the measure $\mu$ different from the set-valued approach \cite{lm}. We prove that the map $f$ is $m_p$-topologically stable if and only if $p$ is a…

We show that for every linear toral automorphism, especially the non-hyperbolic ones, the entropies of ergodic measures form a dense set on the interval from zero to the topological entropy.

We consider random multimodal $C^3$ maps with negative Schwarzian derivative, defined on a finite union of closed intervals in $[0,1]$, onto the interval $[0,1]$ with the base space $\Omega$ and a base invertible ergodic map…

This paper deals with both complex dynamical systems and conformal iterated function systems. We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a $d$-parameter family of…

On a closed Riemannian surface $(M,\bar g)$ with negative Euler characteristic, we study the problem of finding conformal metrics with prescribed volume $A>0$ and the property that their Gauss curvatures $f_\lambda= f + \lambda$ are given…

We consider the harmonic measure on a disconnected polynomial Julia set in terms of Brownian motion. We show that the harmonic measure of any connected component of such a Julia set is zero. Associated to the polynomial is a combinatorial…

For any hyperbolic rational map and any net of Borel probability measures on the space of Borel probability measures on the Julia set, we show that this net satisfies a strong form of the large deviation principle with a rate function given…

Consider a multimodal interval map $f$ of $C^3$ with non-flat critical points. We establish several characterizations of the map $f$ is quasi-symmetrically conjugated to a piecewise affine map in the case $f$ is topologically exact and all…

It is well known that the open set condition and the positivity of the $t$-dimensional Hausdorff measure are equivalent on self-similar sets, where $t$ is the zero of the topological pressure. We prove an analogous result for a class of…