Heterodimensional cycles, partial hyperbolicity and limit dynamics

L. J. Diaz, and J. Rocha. "Heterodimensional cycles, partial hyperbolicity and limit dynamics." Fundamenta Mathematicae 174.2 (2002): 127-186. <http://eudml.org/doc/283373>.

@article{L2002,
abstract = {We study one-parameter families of diffeomorphisms unfolding heterodimensional cycles (i.e. cycles containing periodic points of different indices). We construct an open set of such arcs such that, for a subset of the parameter space with positive relative density at the bifurcation value, the resulting nonwandering set is the disjoint union of two hyperbolic basic sets of different indices and a strong partially hyperbolic set which is robustly transitive. The dynamics of the diffeomorphisms we consider is partially hyperbolic with one-dimensional central direction. The main tool for proving our results is the construction of a one-dimensional model given by an iterated function system which describes the limit dynamics in the central direction. For selected parameters of the arc, we translate properties of the model family to the diffeomorphisms.},
author = {L. J. Diaz, J. Rocha},
journal = {Fundamenta Mathematicae},
keywords = {heteroclinic cycles; nonwandering sets; diffeomorphisms},
language = {eng},
number = {2},
pages = {127-186},
title = {Heterodimensional cycles, partial hyperbolicity and limit dynamics},
url = {http://eudml.org/doc/283373},
volume = {174},
year = {2002},
}

TY - JOUR
AU - L. J. Diaz
AU - J. Rocha
TI - Heterodimensional cycles, partial hyperbolicity and limit dynamics
JO - Fundamenta Mathematicae
PY - 2002
VL - 174
IS - 2
SP - 127
EP - 186
AB - We study one-parameter families of diffeomorphisms unfolding heterodimensional cycles (i.e. cycles containing periodic points of different indices). We construct an open set of such arcs such that, for a subset of the parameter space with positive relative density at the bifurcation value, the resulting nonwandering set is the disjoint union of two hyperbolic basic sets of different indices and a strong partially hyperbolic set which is robustly transitive. The dynamics of the diffeomorphisms we consider is partially hyperbolic with one-dimensional central direction. The main tool for proving our results is the construction of a one-dimensional model given by an iterated function system which describes the limit dynamics in the central direction. For selected parameters of the arc, we translate properties of the model family to the diffeomorphisms.
LA - eng
KW - heteroclinic cycles; nonwandering sets; diffeomorphisms
UR - http://eudml.org/doc/283373
ER -