Abstract
In this chapter we continue the study of multifractal analysis for flows. The emphasis is now on dimension spectra of hyperbolic flows. We first consider the somewhat simpler case of suspension semiflows over expanding maps. It is presented mainly as a motivation for the case of hyperbolic sets for conformal flows, without the additional complication of simultaneously having contraction and expansion. In the case of entropy spectra for hyperbolic flows, we show that the cohomology assumptions required in the study of irregular sets are generically satisfied.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
L. Barreira, Dimension and Recurrence in Hyperbolic Dynamics, Progress in Mathematics 272, Birkhäuser, Basel, 2008.
L. Barreira, Ergodic Theory, Hyperbolic Dynamics and Dimension Theory, Universitext, Springer, Berlin, 2012.
L. Barreira and B. Saussol, Multifractal analysis of hyperbolic flows, Commun. Math. Phys. 214 (2000), 339–371.
L. Barreira and J. Schmeling, Sets of “non-typical” points have full topological entropy and full Hausdorff dimension, Isr. J. Math. 116 (2000), 29–70.
R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphism, Lect. Notes in Math. 470, Springer, Berlin, 1975.
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and Its Applications 54, Cambridge University Press, Cambridge, 1995.
Ya. Pesin and V. Sadovskaya, Multifractal analysis of conformal axiom A flows, Commun. Math. Phys. 216 (2001), 277–312.
J. Schmeling, Entropy preservation under Markov coding, J. Stat. Phys. 104 (2001), 799–815.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Barreira, L. (2013). Multifractal Analysis of Hyperbolic Flows. In: Dimension Theory of Hyperbolic Flows. Springer Monographs in Mathematics. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00548-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-00548-5_8
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00547-8
Online ISBN: 978-3-319-00548-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)