The Smale horseshoes in a class of non-invertible maps in R-3 with two-direction instability

摘要

We study the existence of Smale horseshoes of new type and the uniformly hyperbolic invariant sets for a class of non-invertible maps in three-dimensional Euclidean spaces with the dimension of instability equal to two. Parameter regions are given, for which the map has a horseshoe and a uniformly hyperbolic invariant set on which the map is topologically conjugate to the two-sided fullshift on four symbols.