Abstract
We consider in this chapter the dimension of repellers, which are invariant sets of a hyperbolic noninvertible dynamics. After describing how Markov partitions can be used to model repellers, we present several applications of the nonadditive thermodynamic formalism to the study of their dimension. In particular, we establish lower and upper dimension estimates for a large class of repellers. Among other results, as a simple corollary of this approach we obtain a new proof of the corresponding result in the case of conformal dynamics (in which case the lower and upper dimension estimates coincide).
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© 2011 Springer Basel AG
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Barreira, L. (2011). Dimension Estimates for Repellers. 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_5
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DOI: https://doi.org/10.1007/978-3-0348-0206-2_5
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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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