Chaotic dynamics of three - dimensional Hénon maps that originate from a homoclinic bifurcation

Three-Dimensional HÉnon-like Maps and Wild Lorenz-like attractors

We discuss a rather new phenomenon in chaotic dynamics connected with the fact that some three-dimensional diffeomorphisms can possess wild Lorenz-type strange attractors. These attractors persist for open domains in the parameter space. In particular, we report on the existence of such domains for a three-dimensional Hénon map (a simple quadratic map with a constant Jacobian which occurs in a ...

Generalized Hénon Map and Bifurcations of Homoclinic Tangencies

Abstract. We study two-parameter bifurcation diagrams of the generalized Hénon map (GHM), that is known to describe dynamics of iterated maps near homoclinic and heteroclinic tangencies. We prove the nondegeneracy of codim 2 bifurcations of fixed points of GHM analytically and compute its various global and local bifurcation curves numerically. Special attention is given to the interpretation o...

Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautonomous Hénon Map

Bifurcation structures in maps of Hénon type

We construct a series of n-unimodal approximations to maps of the Hénon type and utilize the associated symbolic dynamics to describe the possible bifurcation structures for such maps. We construct the bifurcation surfaces of the short periodic orbits in the topological parameter space and check numerically that the Hénon map parameter plane (a, b) is topologically equivalent to a two-dimension...

Homoclinic Bifurcations for the Hénon Map

Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. We use this limit to assign global symbols to orbits and use continuation from the limit to study their bifurcations. We find a bound on the parameter range for which the Hénon map exhibits a complete binary horseshoe as well as a subshift of finite type. We classify homoclinic bifurcations, and study tho...