DISCRETE CONLEY INDEX THEORY FOR ZERO DIMENSIONAL BASIC SETS

作者：De Rezende Ketty A^*; Villapouca Mariana G

来源：Discrete and Continuous Dynamical Systems, 2017, 37(3): 1359-1387.

DOI：10.3934/dcds.2017056

• Conley index
• dynamical systems
• homology theory
• diffeomorphisms and connection matrix pair

In this article the discrete Conley index theory is used to study diffeomorphisms on closed differentiable n-manifolds with zero dimensional hyperbolic chain recurrent set. A theorem is established for the computation of the discrete Conley index of these basic sets in terms of the dynamical information contained in their associated structure matrices. Also, a classification of the reduced homology Conley index of these basic sets is presented using its Jordan real form. This, in turn, is essential to obtain a characterization of a pair of connection matrices for a Morse decomposition of zero-dimensional basic sets of a diffeomorphism.

• 出版日期2017-3