Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms

Details Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms

2004-12-08

arxiv.org/abs/math/0412162v1

Mathematics

Dynamical Systems

Scientific paper

We explore the connected/disconnected dichotomy for the Julia set of polynomial automorphisms of C^2. We develop several aspects of the question, which was first studied by Bedford-Smillie. We introduce a new sufficient condition for the connectivity of the Julia set, that carries over for certain H{\'e}non-like and birational maps. We study the structure of disconnected Julia sets and the associated invariant currents. This provides a simple approach to some results of Bedford-Smillie, as well as some new corollaries --the connectedness locus is closed, construction of external rays in the general case, etc. We also prove the following theorem: a hyperbolic polynomial diffeomorphism of C^2 with connected Julia set must have attracting or repelling orbits. This is an analogue of a well known result in one dimensional dynamics.

Affiliated with

Also associated with

No associations

Rating

Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms 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 Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-169994