Related papers: Dirac physical measures on saddle-type fixed point…

We describe the topological structure of closed manifolds of dimension no less than four which admit Morse-Smale diffeomorphisms such that its non-wandering set contains any number of sink periodic points, and any number of source periodic…

The diffeomorphism symmetry of general relativity leads in the canonical formulation to constraints, which encode the dynamics of the theory. These constraints satisfy a complicated algebra, known as Dirac's hypersurface deformation…

We show that for every $C^\infty$ diffeomorphism of a closed Riemannian manifold, if there exists a positive volume set of points which admit some expansion with a positive Lyapunov exponent (in a weak sense) then there exists an invariant…

Given a surface $M$ and a Borel probability measure $\nu$ on the group of $C^2$-diffeomorphisms of $M$, we study $\nu$-stationary probability measures on $M$. We prove for hyperbolic stationary measures the following trichotomy: either the…

The purpose of this paper is to present several examples of non--autonomous basins of attraction that arise from sequences of automorphisms of $\mathbb C^k$. In the first part, we prove that the non-autonomous basin of attraction arising…

In this paper we consider $C^1$ surface diffeomorphisms and study the existence of phase transitions, here expressed by the non-analiticity of the pressure function associated to smooth and geometric-type potentials. We prove that the space…

For $C^0$ generic continuous maps or homeomorphisms on compact Riemannian manifold, we prove that (1) the space of physical-like measures coincides with the set of invariant measures supported on chain recurrent classes, (2) every point in…

In this paper, we prove that ergodic measures with large entropy give uniformly large measure to the set of points with simultaneously long unstable and long stable manifolds. As a consequence, for $C^{\infty}$ surface diffeomorphisms, we…

In the present article we study the periodic structure of some well-known classes of $C^1$ self-maps on the product of spheres of different dimensions: transversal maps, Morse-Smale diffeomorphisms and maps with all its periodic points…

We study the problem of conjugating a diffeomorphism of the interval to (positive) powers of itself. Although this is always possible for homeomorphisms, the smooth setting is rather interesting. Besides the obvious obstruction given by…

We study the orbit behavior of a four dimensional smooth symplectic diffeomorphism $f$ near a homoclinic orbit $\Gamma$ to an 1-elliptic fixed point under some natural genericity assumptions. 1-elliptic fixed point has two real eigenvalues…

In the first part of this text we give a survey of the properties satisfied by the C1-generic conservative diffeomorphisms of compact surfaces. The main result that we will discuss is that a C1-generic conservative diffeomorphism of a…

We study generic volume-preserving diffeomorphisms on compact manifolds. We show that the following property holds generically in the $C^1$ topology: Either there is at least one zero Lyapunov exponent at almost every point, or the set of…

We prove a $C^\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a $C^\infty$ closing lemma for Reeb flows on closed contact three-manifolds, which was recently proved as an application of…

The main result of this paper is that every non-trivial Hamiltonian diffeomorphism of a closed oriented surface of genus at least one has periodic points of arbitrarily high period. The same result is true for S^2 provided the…

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 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…

We prove that a partially hyperbolic attractor for a $C^1$ vector field with two dimensional center supports an SRB measure. In addition, we show that if the vector field is $C^2$, and the center bundle admits the sectional expanding…

Given a piecewise $C^{1+\beta}$ map of the interval, possibly with critical points and discontinuities, we construct a symbolic model for invariant probability measures with nonuniform expansion that do not approach the critical points and…

We construct a $C^\infty$ area-preserving diffeomorphism of the two-dimensional torus which is Bernoulli (in particular, ergodic) with respect to Lebesgue measure, homotopic to the identity, and has a lift to the universal covering whose…