Search

Summary

We introduce a notion of weak Denjoy subsystem (WDS) that generalizes the Aubry–Mather–Cantor sets to diffeomorphisms of manifolds. We explain how a rotation number can be associated to such a WDS. Then we build in any horseshoe a continuous one parameter family of such WDS that is indexed by its rotation number. Looking at the inverse problem in the setting of Aubry– Mather theory, we also prove that for a generic conservative twist map of the annulus, the majority of the Aubry–Mather sets are contained in some horseshoe that is associated to an Aubry–Mather set with a rational rotation number.

We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransversal heteroclinic cycles. We show that bifurcations under consideration lead to the birth of Lorenz-like attractors. They can be viewed as attractors in the Poincare map for periodically perturbed classical Lorenz attractors and hence they can allow for the existence of homoclinic tangencies and wild hyperbolic sets.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

Denjoy subsystems and horseshoes

Summary

On Global Bifurcations of Three-dimensional Diffeomorphisms Leading to Lorenz-like Attractors

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

Denjoy subsystems and horseshoes

Summary

On Global Bifurcations of Three-dimensional Diffeomorphisms Leading to Lorenz-like Attractors