Related papers: Sur la construction de mesures selles

We prove that for a polynomial diffeomorphism of C^2 , the support of any invariant measure, apart from a few obvious cases, is contained in the closure of the set of saddle periodic points.

We build measurable holomorphic motions for Julia sets of holomorphic families of endomorphisms of CP(k) under various equivalent notions of stability.

The aim of this paper is to present examples of Kahler holomorphically pseudosymmetric metrics on the projective space CP^n.

We give a method for constructing (possible large) self--small modules via some special homomorphisms of rings, called here weak epimorphisms.

We study the laminarity of the Green current of endomorphisms of $P^2C$ near hyperbolic measures of saddle type. When these measures are supported by attracting sets, we prove that the Green current is laminar in the basin of attraction and…

We study stable conditional measures for a certain equilibrium measure for hyperbolic endomorphisms, on basic sets with overlaps; we show that these conditional measures are geometric probabilities and measures of maximal stable dimension.…

Let $f$ be an holomorphic endomorphism of $\mathbb{C}\mathbb{P}^k$. We construct by using coding techniques a class of ergodic measures as limits of non-uniform probability measures on preimages of points. We show that they have large…

We construct diffeomorphisms in dimension $d\geq 2$ exhibiting $C^1$-robust heteroclinic tangencies.

We consider the case of hyperbolic basic sets $\Lambda$ of saddle type for holomorphic maps $f: \mathbb P^2\mathbb C \to \mathbb P^2\mathbb C$. We study equilibrium measures $\mu_\phi$ associated to a class of H\"older potentials $\phi$ on…

We prove that for a polynomial diffeomorphism of C^2, uniform hyperbolicity on the set of saddle periodic points implies that saddle points are dense in the Julia set. In particular f satisfies Smale's Axiom A on C^2 .

We construct $C^2$-robust homoclinic and heterodimensional tangencies of large codimension inside transitive partially hyperbolic sets.

We study random holomorphic endomorphisms of P^k(C). This article is the second part of arXiv:1205.1601

The deformation problem for pseudoholomorphic curves and related geometrical properties of the total moduli space of pseudoholomorphic curves are studied. A sufficient condition for the saddle point property of the total moduli space is…

For a hyperbolic polynomial automorphism of $\C^2$, we show the existence of a measure of maximal dimension, and identify the conditions under which a measure of full dimension exists.

The embedding of the isometry group of the coset spaces SU(1,n)/ U(1)xSU(n) in Sp(2n+2,R) is discussed. The knowledge of such embedding provides a tool for the determination of the holomorphic prepotential characterizing the special…

We construct partially hyperbolic diffeomorphisms having semi-local robustly transitive sets with $C^1$-robust cycles of any co-index. These constructions also provide a new method to create $C^2$-robust homoclinic, equidimensional and…

We present a construction of a proper holomorphic embedding $f\colon \Bbb P^1\setminus C\hookrightarrow \Bbb C^2$, where C is a Cantor set obtained by removing smaller and smaller vertical and horizontal strips from a square of side 2,…

We consider dynamical systems generated by partially hyperbolic surface endomorphisms of class C^r with one-dimensional strongly unstable subbundle. As the main result, we prove that such a dynamical system generically admits finitely many…

In this article we study some statistical aspects of surface diffeomorphisms. We first show that for a $C^1$ generic diffeomorphism, a Dirac invariant measure whose \emph{statistical basin of attraction} is dense in some open set and has…

We study random holomorphic endomorphisms of P^k(C). Under some assumptions, we construct a random Green current and a random Green measure and we prove that these measures have mixing properties.