Abstract
In this chapter we establish a conditional variational principle for flows with a locally maximal hyperbolic set. In other words, we express the topological entropy of the level sets of the Birkhoff averages of a given function in terms of a conditional variational principle. As an application of this principle, we establish the analyticity of several classes of multifractal spectra for hyperbolic flows. In particular, we consider the multifractal spectra for the local entropies and for the Lyapunov exponents.
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Barreira, L. (2013). Entropy Spectra. In: Dimension Theory of Hyperbolic Flows. Springer Monographs in Mathematics. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00548-5_9
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DOI: https://doi.org/10.1007/978-3-319-00548-5_9
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00547-8
Online ISBN: 978-3-319-00548-5
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