Abstract

In this chapter, again for conformal hyperbolic flows, we establish an explicit formula for the pointwise dimension of an arbitrary invariant measure in terms of the local entropy and the Lyapunov exponents. In particular, this formula allows us to show that the Hausdorff dimension of a (nonergodic) invariant measure is equal to the essential supremum of the Hausdorff dimensions of the measures in each ergodic decomposition. We also discuss the problem of the existence of invariant measures of maximal dimension. These are measures at which the supremum of the Hausdorff dimensions over all invariant measures is attained.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call