Accessability of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps

Details Accessability of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps Accessability of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps

1993-03-20

arxiv.org/abs/math/9303209v1

Mathematics

Dynamical Systems

Scientific paper

We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, if $A$ is completely invariant (i.e. $f^{-1}(A)=A$), and if $\mu$ is an arbitrary $f$-invariant measure with positive Lyapunov exponents on the boundary of $A$, then $\mu$-almost every point $q$ in the boundary of $A$ is accessible along a curve from $A$. In fact we prove the accessability of every "good" $q$ i.e. such $q$ for which "small neighbourhoods arrive at large scale" under iteration of $f$. This generalizes Douady-Eremenko-Levin-Petersen theorem on the accessability of periodic sources.

Affiliated with

Also associated with

No associations

Rating

Accessability of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps 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 Accessability of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Accessability of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-517041