Heterodimensional cycles, partial hyperbolicity and limit dynamics
Copyright policy )Heterodimensional cycles, partial hyperbolicity and limit dynamics
A one-parametric family of diffeomorphisms is studied unfolding heteroclinic cycles. An open set of such arcs is constructed such that the resulting nonwandering set is the disjont union of two hyperbolic basis sets of different indices and a strong partially hyperbolic set which is robustly transitive. The dynamics of diffeomorphisms is partially hyperbolic with one-dimensional central direction. The main tool of the proof is the construction of a one-dimensional model given by an iterated function system which describes the limit dynamics in the central direction.
diffeomorphisms, Infinite nonwandering sets arising in bifurcations of dynamical systems, nonwandering sets, Homoclinic and heteroclinic orbits for dynamical systems, heteroclinic cycles, Partially hyperbolic systems and dominated splittings, Bifurcations connected with nontransversal intersection in dynamical systems
diffeomorphisms, Infinite nonwandering sets arising in bifurcations of dynamical systems, nonwandering sets, Homoclinic and heteroclinic orbits for dynamical systems, heteroclinic cycles, Partially hyperbolic systems and dominated splittings, Bifurcations connected with nontransversal intersection in dynamical systems
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