相关论文: Complex Dynamics of birational maps of $\mathbb{P}…

We show that any birational selfmap of a complex projective surface that has dynamical degree greater than one and is defined over a number field automatically satisfies the Bedford-Diller energy condition after a suitable birational…

We develop the study of some spaces of currents of bidegree (p,p). As an application we construct the equilibrium measure for a large class of birational maps of P^k as intersection of Green currents. We show that these currents are…

We study the dynamics of meromorphic maps for a compact Kaehler manifold X. More precisely, we give a simple criterion that allows us to produce a measure of maximal entropy. We can apply this result to bound the Lyapunov exponents. Then,…

We provide conditions which guarantee that ergodic measures are dense in the simplex of invariant probability measures of a dynamical system given by a continuous map acting on a Polish space. Using them we study generic properties of…

For any 1-lipschitz ergodic map $F:\; \mathbb{Z}^{k}_{p} \mapsto \mathbb{Z}^{k}_{p},\;k>1\in\mathbb{N},$ there are 1-lipschitz ergodic map $G:\; \mathbb{Z}_{p} \mapsto \mathbb{Z}_{p}$ and two bijection $H_k$, $T_{k,\;P}$ that $$G = H_{k}…

We prove that under the natural assumption over the dynamical degrees, the saddle periodic points of a H\'enon-like map in any dimension equidistribute with respect to the equilibrium measure. Our work is a generalization of results of…

We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…

We study the ergodic properties of generic continuous dynamical systems on compact manifolds. As a main result we prove that generic homeomorphisms have convergent Birkhoff averages under continuous observables at Lebesgue almost every…

For meromorphic maps of complex manifolds, ergodic theory and pluripotential theory are closely related. In nice enough situations, dynamically defined Green's functions give rise to invariant currents which intersect to yield measures of…

We consider a dynamics of a generic birational plane map \Phi_n: CP^2 \to CP^2, CP^2 -image of the birational mapping (inverse map is also rational)F_n : C^2 \to C^2 and its such important characteristic as the Arnold complexity C_A(k),…

We study the map from conductances to edge energies for harmonic functions on finite graphs with Dirichlet boundary conditions. We prove that for any compatible acyclic orientation and choice of energies there is a unique choice of…

Since the end of the XIXth century, we know that each birational map of the complex projective plane is the product of a finite number of quadratic birational maps of the projective plane; this motivates our work which essentially deals…

Let f be a self-map of a compact manifold M, admitting an global SRB measure \mu. For a continuous test function \phi on M and a constant \alpha>0, consider the set of the initial points for which the Birkhoff time averages of the function…

When a birational surface map is expanding on cohomology there is a canonical way to associate positive closed currents to the map and its inverse. In this paper we use a version of Dirichlet energy to construct the wedge product of these…

In this paper we describe the dynamics of certain rational maps of the form $k \cdot (x+x^{-1})$ over finite fields of odd characteristic.

In this paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on…

We consider the ergodic theory of plane rational maps that preserve the natural holomorphic volume form on the algebraic torus. Specifically we construct natural invariant probability measures for a large class of such maps by intersecting…

Based on the Carath\'eodory -Pesin structure theory[11], we introduce three notions of topological pressure of a proper map and provide some properties of these notions. For the proper map of a locally compact separable metric space, we…

Expanding Thurston maps were introduced by M. Bonk and D. Meyer with motivation from complex dynamics and Cannon's conjecture from geometric group theory via Sullivan's dictionary. In this paper, we study subsystems of expanding Thurston…

By a result of Blokh from 1984, every transitive map of a tree has the relative specification property, and so it has finite decomposition ideal, positive entropy and dense periodic points. In this paper we construct a transitive dendrite…