Multifractal Analysis of Hyperbolic Flows
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.
KeywordsGibbs Measure Topological Entropy Multifractal Analysis Dimension Spectrum Markov Partition
- 28.R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphism, Lect. Notes in Math. 470, Springer, Berlin, 1975. Google Scholar