For any C 1 diffeomorphism with dominated splitting we consider a nonempty set of invariant measures which describes the asymptotic statistics of Lebesguealmost all orbits. They are the limits of convergent subsequences of averages of the Dirac delta measures supported on those orbits. We prove that the metric entropy of each of these measures is bounded from below by the sum of the Lyapunov exponents on the dominating subbundle. As a consequence, if those exponents are non negative, and if the exponents on the dominated subbundle are non positive, those measures satisfy the Pesin Entropy Formula.

Let M be a compact metric space and g : M → M be an homeomorphism C 0 -close to an expansive map of M. In general, it is not true that g is also expansive, but it still has some properties resembling the expansivity. In fact, if we identify pairs of points whose g-orbits stay nearby, both for the future and the past, we obtain an equivalence relation ∼. The quotient space M/ ∼ is a compact, metric space and g induces an expansive homeomorphism g on that quotient. If M is a surface, we show that for any x ∈ M/ ∼ the connected component of the local stable (unstable) set containing x is nontrivial and arc-wise connected.

We consider C 1 Anosov diffeomorphisms on a compact Riemannian manifold. We define the weak pseudo-physical measures, which include the physical measures when these latter exist. We prove that ergodic weak pseudophysical measures do exist, and that the set of invariant probability measures that satisfy Pesin's Entropy Formula is the weak * -closed convex hull of the ergodic weak pseudo-physical measures. In brief, we give in the C 1 -scenario of uniform hyperbolicity, a characterization of Pesin's Entropy Formula in terms of physical-like properties.

Estudio del contenido de selenio en carne vacuna luego del proceso de cocción Study of the selenium content in beef after the cooking process Estudo do teor de selênio na carne bovina após o processo de cozimento

We prove that the C 3 diffeomorphisms on surfaces, exhibiting infinitely many sinks near the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of C 3 diffeomorphisms such that infinitely many sinks persist simultaneously. On the other hand, if they are perturbed along one-parameter families that unfold generically the quadratic tangencies, then at most a finite number of those sinks have continuation. *