Almost every real quadratic map is either regular or stochastic

Details Almost every real quadratic map is either regular or stochastic Almost every real quadratic map is either regular or stochastic

1997-07-15

arxiv.org/abs/math/9707224v1

Mathematics

Dynamical Systems

Scientific paper

We prove uniform hyperbolicity of the renormalization operator for all possible real combinatorial types. We derive from it that the set of infinitely renormalizable parameter values in the real quadratic family $P_c: x\mapsto x^2+c$ has zero measure. This yields the statement in the title (where ``regular'' means to have an attracting cycle and ``stochastic'' means to have an absolutely continuous invariant measure). An application to the MLC problem is given.

Affiliated with

Also associated with

No associations

Rating

Almost every real quadratic map is either regular or stochastic 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 Almost every real quadratic map is either regular or stochastic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Almost every real quadratic map is either regular or stochastic will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-399673