# American Institute of Mathematical Sciences

April  2006, 14(2): 355-363. doi: 10.3934/dcds.2006.14.355

## A note about stable transitivity of noncompact extensions of hyperbolic systems

 1 Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH 2 Department of Mathematics, West Chester University, West Chester, PA 19383, United States 3 Department of Mathematics, University of Houston, Houston, TX 77204-3008

Received  November 2004 Revised  February 2005 Published  November 2005

Let $f:X\to X$ 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 $C^2$ $G$-extensions of $f$ there exists an open and dense subset of stably transitive transformations. If $G=K\times \mathbb R^n$, where $K$ is a compact connected Lie group, we show that an open and dense set of $C^2$ $G$-extensions satisfying a certain separation condition are transitive. The separation condition is necessary.
Citation: Ian Melbourne, V. Niţicâ, Andrei Török. A note about stable transitivity of noncompact extensions of hyperbolic systems. Discrete & Continuous Dynamical Systems - A, 2006, 14 (2) : 355-363. doi: 10.3934/dcds.2006.14.355
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