Bowen's equation in the non-uniform setting

Details Bowen's equation in the non-uniform setting Bowen's equation in the non-uniform setting

2009-08-28

arxiv.org/abs/0908.4126v2

Ergodic Theory and Dynamical Systems (2011), 31: 1163-1182

Mathematics

Dynamical Systems

23 pages, 1 figure: v2 has expanded introduction; "bounded" contraction replaced with "tempered"; Section 4, Proposition 5.1 a

Scientific paper

10.1017/S0143385710000362

We show that Bowen's equation, which characterises the Hausdorff dimension of certain sets in terms of the topological pressure of an expanding conformal map, applies in greater generality than has been heretofore established. In particular, we consider an arbitrary subset Z of a compact metric space and require only that the lower Lyapunov exponents be positive on Z, together with a tempered contraction condition. Among other things, this allows us to compute the dimension spectrum for Lyapunov exponents for maps with parabolic periodic points, and to relate the Hausdorff dimension to the topological entropy for arbitrary subsets of symbolic space with the appropriate metric.

Affiliated with

Also associated with

No associations

Rating

Bowen's equation in the non-uniform setting does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bowen's equation in the non-uniform setting, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bowen's equation in the non-uniform setting will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-192914