Dynamical approximation and kernels of nonescaping-hyperbolic components

Details Dynamical approximation and kernels of nonescaping-hyperbolic components Dynamical approximation and kernels of nonescaping-hyperbolic components

2009-10-05

arxiv.org/abs/0910.0743v1

Ergodic Theory and Dynamical Systems 2012

Mathematics

Dynamical Systems

16 pages, 1 figure

Scientific paper

10.1017/S0143385711000162

Let F_n be families of entire functions, holomorphically parametrized by a complex manifold M. We consider those parameters in M that correspond to nonescaping-hyperbolic functions, i.e., those maps f in F_n for which the postsingular set P(f) is a compact subset of the Fatou set F(f) of f. We prove that if F_n converge to a family F in the sense of a certain dynamically sensible metric, then every nonescaping-hyperbolic component in the parameter space of F is a kernel of a sequence of nonescaping-hyperbolic components in the parameter spaces of F_n. Parameters belonging to such a kernel do not always correspond to hyperbolic functions in F. Nevertheless, we show that these functions must be J-stable. Using quasiconformal equivalences, we are able to construct many examples of families to which our results can be applied.

Affiliated with

Also associated with

No associations

Rating

Dynamical approximation and kernels of nonescaping-hyperbolic components 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 Dynamical approximation and kernels of nonescaping-hyperbolic components, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamical approximation and kernels of nonescaping-hyperbolic components will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-9873