Abstract
In this chapter, for conformal flows with a hyperbolic set, we establish a conditional variational principle for the dimension spectra of Birkhoff averages. The main novelty in comparison to the former chapters is that we consider simultaneously Birkhoff averages into the future and into the past. The main difficulty is that even though the local product structure is bi-Lipschitz, the level sets of the Birkhoff averages are not compact. Our proof is based on the use of Markov systems and is inspired by earlier arguments in the case of discrete time.
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Barreira, L. (2013). Dimension Spectra. In: Dimension Theory of Hyperbolic Flows. Springer Monographs in Mathematics. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00548-5_11
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DOI: https://doi.org/10.1007/978-3-319-00548-5_11
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00547-8
Online ISBN: 978-3-319-00548-5
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