Lyapunov exponents, bifurcation currents and laminations in bifurcation loci

Details Lyapunov exponents, bifurcation currents and laminations in bifurcation loci Lyapunov exponents, bifurcation currents and laminations in bifurcation loci

2008-01-17

arxiv.org/abs/0801.2590v1

Mathematics

Complex Variables

Scientific paper

Bifurcation loci in the moduli space of degree $d$ rational maps are shaped by the hypersurfaces defined by the existence of a cycle of period $n$ and multiplier 0 or $e^{i\theta}$. Using potential-theoretic arguments, we establish two equidistribution properties for these hypersurfaces with respect to the bifurcation current. To this purpose we first establish approximation formulas for the Lyapunov function. In degree $d=2$, this allows us to build holomorphic motions and show that the bifurcation locus has a lamination structure in the regions where an attracting basin of fixed period exists.

Affiliated with

Also associated with

No associations

Rating

Lyapunov exponents, bifurcation currents and laminations in bifurcation loci 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 Lyapunov exponents, bifurcation currents and laminations in bifurcation loci, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lyapunov exponents, bifurcation currents and laminations in bifurcation loci will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-392402