Stable transitivity of certain noncompact extensions of hyperbolic systems

Disc. Cont. Dyn. Syst. 14 (2006) 355-363.

Ian Melbourne, Viorel Niţică and Andrei Török

Abstract

Let f:X->X be the restriction to a hyperbolic basic set of a smooth diffeomorphism. If G is the special Euclidean group SE(2) we show that in the set of C² G-extensions of f there exists an open and dense subset of stably transitive transformations. If G=KxRⁿ, where K is a compact connected Lie group, we show that an open and dense set of C² G-extensions satisfying a certain separation condition are transitive. The separation condition is necessary.