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Repellers and Hyperbolic Sets

Part of the Progress in Mathematics book series (PM, volume 272)

Abstract

We start in this chapter the study of the dimension of hyperbolic invariant sets of conformal dynamical systems (both invertible and noninvertible). As we observed in Section 3.1, one of the motivations for the study of geometric constructions is precisely the study of the dimension of invariant sets of hyperbolic dynamics. We show in this chapter that indeed a similar approach can be effected for repellers and hyperbolic sets of conformal maps, using Markov partitions and essentially following the arguments for geometric constructions in Chapter 3.

Keywords

Gibbs Measure Equilibrium Measure Geometric Construction Markov Partition Topological Pressure 
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Copyright information

© Birkhäuser Verlag AG 2008

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