Abstract
In this chapter we present a multidimensional multifractal analysis for hyperbolic flows. More precisely, we consider multifractal spectra associated to multidimensional parameters, obtained from computing the entropy of the level sets associated to several Birkhoff averages. These spectra exhibit several new phenomena that are absent in 1-dimensional multifractal analysis. We also consider the more general class of flows with upper semicontinuous entropy. In this chapter the multifractal analysis is obtained from a conditional variational principle for the topological entropy of the level sets.
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L. Barreira and P. Doutor, Birkhoff averages for hyperbolic flows: variational principles and applications, J. Stat. Phys. 115 (2004), 1567–1603.
L. Barreira and B. Saussol, Variational principles for hyperbolic flows, Fields Inst. Commun. 31 (2002), 43–63.
L. Barreira, B. Saussol and J. Schmeling, Higher-dimensional multifractal analysis, J. Math. Pures Appl. 81 (2002), 67–91.
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Barreira, L. (2013). Multidimensional Spectra. In: Dimension Theory of Hyperbolic Flows. Springer Monographs in Mathematics. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00548-5_10
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DOI: https://doi.org/10.1007/978-3-319-00548-5_10
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00547-8
Online ISBN: 978-3-319-00548-5
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