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Article Contents

# Discrete conley index theory for zero dimensional basic sets

• * Corresponding author
The first author is partially supported by CNPq under grant 309734/2014-2 and by FAPESP under grant 2012/18780-0.
• 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.

Mathematics Subject Classification: Primary:37B30, 37B10, 37C05;Secondary:37D15, 37D05, 37B35.

 Citation:

• Figure 1.  Braid diagram

Figure 2.  Graded module braids with endomorphisms 1

Figure 3.  Graded module braids with endomorphisms 2

Figure 4.  Smale's Horseshoe

Figure 5.  fitted diffeomorphism

Figure 6.  Smale diffeomorphism

Figure 7.  Connection matrix pair for zero-dimensional basic sets decomposition

Figure 8.  Representation of a connection matrix pair for a zero-dimensional basic set decomposition

Figure 9.  Fitted diffeomorphism

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