Given a dynamical system (X, f), a basic property that one may study is topological transitivity, that is the existence of a dense forward We emphasize that in this paper, X will be mostly a non-compact set and f will be invertible. Keywords: stable topological transitivity hyperbolic system Anosov diffeomorphism extension with Lie group fiberĪ dynamical system is a continuous map f of a topological space X. The paper lists several open problems and conjectures and tries to place this topic of research in the general context of hyperbolic and topological dynamics. In particular, we address the stability and genericity of topological transitivity in large classes of such transformations. The hyperbolic systems we consider are mostly discrete time. The goal of this review article is to present the state of the art for the class of Holder extensions of hyperbolic systems with non-compact connected Lie group fiber. Even though this is one of the most basic dynamical properties that can be investigated, the tools used by various authors are quite diverse and are strongly related to the class of dynamical systems under consideration. ![]() Received: 12 December 2014 /Accepted: 26 January 2015 /Published: 4 February 2015Ībstract: Currently, there is great renewed interest in proving the topological transitivity of various classes of continuous dynamical systems. Box 1-764, R0-70700 Bucharest, Romaniaģĝepartment of Mathematics, University of Houston, 651 PGH, Houston, TX 77204-3008, USA E-Mail: Author to whom correspondence should be addressed E-Mail: Tel.: +61. Open and Dense Topological Transitivity of Extensions by Non-Compact Fiber of Hyperbolic Systems: A Reviewġĝepartment of Mathematics, West Chester University, West Chester, PA 19383, USAĢ Institute of Mathematics of the Romanian Academy, P.O.
0 Comments
Leave a Reply. |