Equilibrium measures on saddle sets of holomorphic maps on P^2

Details Equilibrium measures on saddle sets of holomorphic maps on P^2 Equilibrium measures on saddle sets of holomorphic maps on P^2

2012-03-14

arxiv.org/abs/1203.3145v1

Mathematics

Dynamical Systems

Scientific paper

We consider the case of hyperbolic basic sets $\Lambda$ of saddle type for holomorphic maps $f: \mathbb P^2\mathbb C \to \mathbb P^2\mathbb C$. We study equilibrium measures $\mu_\phi$ associated to a class of H\"older potentials $\phi$ on $\Lambda$, and find the measures $\mu_\phi$ of iterates of arbitrary Bowen balls. Estimates for the pointwise dimension $\delta_{\mu_\phi}$ of $\mu_\phi$ that involve Lyapunov exponents and a correction term are found, and also a formula for the Hausdorff dimension of $\mu_\phi$ in the case when the preimage counting function is constant on $\Lambda$. For terminal/minimal saddle sets we prove that an invariant measure $\nu$ obtained as a wedge product of two positive closed currents, is in fact the measure of maximal entropy for the \textit{restriction} $f|_\Lambda$. This allows then to obtain formulas for the measure $\nu$ of arbitrary balls, and to give a formula for the pointwise dimension and the Hausdorff dimension of $\nu$.

Affiliated with

Also associated with

No associations

Rating

Equilibrium measures on saddle sets of holomorphic maps on P^2 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 Equilibrium measures on saddle sets of holomorphic maps on P^2, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equilibrium measures on saddle sets of holomorphic maps on P^2 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-716075