Related papers: Equidistribution for meromorphic maps with dominan…

Let $f$ be a holomorphic endomorphism of $\mathbb P^k$ of algebraic degree $d\geq 2$. We show that the periodic points of $f$ of period $n$ equidistribute towards the equilibrium measure of $f$ exponentially fast as $n$ tends to infinity.…

Let (F_n) be a sequence of (multivalued) meromorphic maps between compact Kaehler manifolds X1 and X2. We study the asymptotic distribution of preimages of points by F_n and the asymptotic distribution of fixed points for multivalued…

Let $G$ be a semisimple Lie group without compact factor and $\Gamma < G$ a torsion-free, cocompact, irreducible lattice. According to Selberg, periodic orbits of regular Weyl chamber flows live on maximal flat periodic tori of the space of…

Let $f:\mathbb{CP}^2\dashrightarrow\mathbb{CP^2}$ be a rational map with algebraic and topological degrees both equal to $d\geq 2$. Little is known in general about the ergodic properties of such maps. We show here, however, that for an…

We consider the dynamics of `nonlinear tent maps': piecewise smooth unimodal maps with nowhere vanishing derivative. We show that if a nonlinear tent map $f$ is not infinitely renormalizable, then all its periodic orbits of sufficiently…

We give a counterexample to the following conjecture: the set of isolated periodic points of an automorphism of degree at least two on an affine space is a set of bounded height. As a positive result, we prove that any cohomologically…

We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to the appearance of…

We give a brief survey on the entropy of holomorphic self maps $f$ of compact K\"ahler manifolds, and rational dominating self maps $f$ of smooth projective varieties. We emphasize the connection between the entropy and the spectral radii…

We first introduce the class of quasi-algebraically stable meromorphic maps of $\P^k.$ This class is strictly larger than that of algebraically stable meromorphic self-maps of $\P^k.$ Then we prove that all maps in the new class enjoy a…

We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…

We consider area preserving maps of surfaces and extend Mather's result on the equality of the closure of the four branches of saddles. He assumed elliptic fixed points to be Moser stable, while we require only that the derivative at this…

We extend the Dinh-Sibony notion of densities of currents to the setting where the ambient manifold is not necessarily K\"ahler and study the intersection of analytic sets from the point of view of densities of currents. As an application,…

We continue our study of the dynamics of meromorphic mappings with small topological degree on a compact K\"ahler surface $X$. Under general hypotheses we are able to construct a canonical invariant measure which is mixing, does not charge…

Let $f$ be a meromorphic function with bounded set of singular values and for which infinity is a logarithmic singularity. Then we show that $f$ has infinitely many repelling periodic points for any minimal period $n\geq1$, using a much…

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…

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…

This paper is an interval dynamics counterpart of three theories founded earlier by the authors, S. Smirnov and others in the setting of the iteration of rational maps on the Riemann sphere: the equivalence of several notions of non-uniform…

For the class of differentiable maps of the plane and, in particular, for standard-like maps (McMillan form), a simple relation is shown between the directions of the local invariant manifolds of a generic point and its contribution to the…

We prove that a $C^{\infty}$-generic area-preserving diffeomorphism of a closed, oriented surface admits a sequence of equidistributed periodic orbits. This is a quantitative refinement of the recently established generic density theorem…

In this note we study some properties of topological entropy for non-compact non-metrizable spaces. We prove that if a uniformly continuous self-map $f$ of a uniform space has topological shadowing property then the map $f$ has positive…