Abstract
This chapter is dedicated to the study of the dimension of a locally maximal hyperbolic set for a conformal flow. We first consider the dimensions along the stable and unstable manifolds and we compute them in terms of the topological pressure. We also show that the Hausdorff dimension and the lower and upper box dimensions of the hyperbolic set coincide and that they are obtained by adding the dimensions along the stable and unstable manifolds, plus the dimension along the flow. This is a consequence of the conformality of the flow. The proofs are based on the use of Markov systems.
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References
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Barreira, L. (2013). Dimension of Hyperbolic Sets. In: Dimension Theory of Hyperbolic Flows. Springer Monographs in Mathematics. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00548-5_5
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DOI: https://doi.org/10.1007/978-3-319-00548-5_5
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00547-8
Online ISBN: 978-3-319-00548-5
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