# American Institute of Mathematical Sciences

July  2011, 29(3): 1197-1204. doi: 10.3934/dcds.2011.29.1197

## Stable transitivity for extensions of hyperbolic systems by semidirect products of compact and nilpotent Lie groups

 1 Department of Mathematics, West Chester University of Pennsylvania, West Chester, PA 19383, United States

Received  January 2010 Revised  May 2010 Published  November 2010

Assume that $X$ is a hyperbolic basic set for $f:X\to X$. We show new examples of Lie group fibers $G$ for which, in the class of $C^r, r>0,$ $G$-extensions of $f$, those that are transitive are open and dense. The fibers are semidirect products of compact and nilpotent groups.
Citation: Viorel Niţică. Stable transitivity for extensions of hyperbolic systems by semidirect products of compact and nilpotent Lie groups. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 1197-1204. doi: 10.3934/dcds.2011.29.1197
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