33 research outputs found
Non uniform hyperbolicity and elliptic dynamics
We present some constructions that are merely the fruit of combining recent
results from two areas of smooth dynamics: nonuniformly hyperbolic systems and
elliptic constructions.Comment: 6 pages, 0 figur
A Closing Lemma for a Class of Symplectic Diffeomorphisms
We prove a closing lemma for a class of partially hyperbolic symplectic
diffeomorphisms. We show that for a generic symplectic diffeomorphism, , with two dimensional center and close to a product map, the set
of all periodic points is dense
On the Plaque Expansivity Conjecture
It is one of the main properties of uniformly hyperbolic dynamics that points
of two distinct trajectories cannot be uniformly close one to another. This
characteristics of hyperbolic dynamics is called expansivity. Hirsch, Pugh and
Shub, 1977, formulated the so-called Plaque Expansivity Conjecture, assuming
that two invariant sequences of leaves of central manifolds, corresponding to a
partially hyperbolic diffeomorphism, cannot be locally close. There are many
important statements in the theory of partial hyperbolicity that can be proved
provided Plaque Expansivity Conjecture holds true. Here we are proving this
conjecture in its general form.Comment: The proof written here was wrong. I hope to replace this with a
correct on