Related papers: Characterization of hyperbolic potentials

We prove that if $f$ is a $C^{1+}$ partially hyperbolic diffeomorphism satisfying certain conditions then there is a $C^1$-open neighborhood $\cA$ of $f$ so that every $g\in \cA\cap \operatorname{Diff}^{1+}(M)$ has a unique equilibrium…

We introduce a class of continuous maps $f$ of a compact topological space $X$ admitting inducing schemes of hyperbolic type and describe the associated tower constructions. We then establish a thermodynamic formalism, i.e., we describe a…

Let $\ast$ and $\widetilde {\ast}$ denote the convolution of two analytic maps and that of an analytic map and a harmonic map respectively. Pokhrel [1] proved that if $f = h+\overline{g}$ is a harmonic map convex in the direction of…

We introduce a class of continuous maps f of a compact metric space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamical formalism, i.e., describe a class of real-valued…

Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…

We consider a robust class of random non-uniformly expanding local homeomorphisms and H\"older continuous potentials with small variation. For each element of this class we develop the Thermodynamical Formalism and prove the existence and…

We consider families of multimodal interval maps with polynomial growth of the derivative along the critical orbits. For these maps Bruin and Todd have shown the existence and uniqueness of equilibrium states for the potential…

We study open zooming systems and potentials with uniqueness of equilibrium states. The uniqueness is established for a certain class of zooming potentials when the map is topologically exact, including the null one. Also, with equilibrium…

It is well-known that for expansive maps and continuous potential functions, the specification property (for the map) and the Bowen property (for the potential) together imply the existence of a unique equilibrium state. We consider…

Let $K$ denote either $\mathbb{R}$ or $\mathbb{C}$. In this article, we introduce two new equivariants associated to a rational map $f\in K(z)$. These objects naturally live on a real hyperbolic space, and carry information about the action…

We show some level-2 large deviation principles for rational maps satisfying a strong form of non-uniform hyperbolicity, called "Topological Collet-Eckmann". More precisely, we prove a large deviation principle for the distribution of…

Given a multimodal interval map $f:I \to I$ and a H\"older potential $\phi:I \to \mathbb{R}$, we study the dimension spectrum for equilibrium states of $\phi$. The main tool here is inducing schemes, used to overcome the presence of…

A rational map $\phi: \mathbb{P}_k^m \dashrightarrow \mathbb{P}_k^n$ is defined by homogeneous polynomials of a common degree $d$. We establish a linear bound in terms of $d$ for the number of $(m-1)$-dimensional fibers of $\phi$, by using…

The purpose of this letter is to point out that some conclusions in the paper (Eur. Phys. J. C {\bf 76}, 324(2016)) are incomplete, and to give complete and improved conclusions. The analytic necessary and sufficient conditions are given…

We completely describe the equilibrium states of a class of potentials over the full shift which includes Falconer's singular value function for affine iterated function systems with invertible affinities. We show that the number of…

In the case of smooth non-invertible maps which are hyperbolic on folded basic sets $\Lambda$, we give approximations for the Gibbs states (equilibrium measures) of arbitrary H\"{o}lder potentials, with the help of weighted sums of atomic…

A classical problem in Complex Dynamics on hyperbolic domains is to characterize the hyperbolic step of parabolic functions. This topic has been studied by several authors, leading to different results and providing characterizations that…

In this paper, we derive a local unique continuation property for stochastic hyperbolic equations without boundary conditions. This result is proved by a global Carleman estimate.

We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local homeomorphisms on compact manifolds and Holder continuous potentials with not very large oscillation. No Markov structure is…

Given a hyperbolic homeomorphism on a compact metric space, consider the space of linear cocycles over this base dynamics which are H\"older continuous and whose projective actions are partially hyperbolic dynamical systems. We prove that…