Abstract
We consider in this chapter the dimension of hyperbolic sets, which are invariant sets of a hyperbolic invertible dynamics. The main aim is to develop as much as possible a corresponding theory to that in Chapter 5 in the case of repellers. In particular, after describing how Markov partitions can be used to model hyperbolic sets, we present several applications of the nonadditive thermodynamic formalism to the study of their dimension. In particular, we obtain lower and upper dimension estimates for a large class of hyperbolic sets, also of maps that need not be differentiable.
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© 2011 Springer Basel AG
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Barreira, L. (2011). Dimension Estimates for Hyperbolic Sets. In: Thermodynamic Formalism and Applications to Dimension Theory. Progress in Mathematics, vol 294. Springer, Basel. https://doi.org/10.1007/978-3-0348-0206-2_6
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DOI: https://doi.org/10.1007/978-3-0348-0206-2_6
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Publisher Name: Springer, Basel
Print ISBN: 978-3-0348-0205-5
Online ISBN: 978-3-0348-0206-2
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