Cubic Critical Portraits and Polynomials with Wandering Gaps

Details Cubic Critical Portraits and Polynomials with Wandering Gaps Cubic Critical Portraits and Polynomials with Wandering Gaps

2010-03-23

arxiv.org/abs/1003.4467v3

Mathematics

Dynamical Systems

31 pages, 4 figures; this is the last, third version of the paper which is to appear in Ergodic Theory and Dynamical Systems

Scientific paper

Thurston introduced $\si_d$-invariant laminations (where $\si_d(z)$ coincides with $z^d:\ucirc\to \ucirc$, $d\ge 2$) and defined \emph{wandering $k$-gons} as sets $\T\subset \ucirc$ such that $\si_d^n(\T)$ consists of $k\ge 3$ distinct points for all $n\ge 0$ and the convex hulls of all the sets $\si_d^n(\T)$ in the plane are pairwise disjoint. He proved that $\si_2$ has no wandering $k$-gons. Call a lamination with wandering $k$-gons a \emph{WT-lamination}. In a recent paper it was shown that uncountably many cubic WT-laminations, with pairwise non-conjugate induced maps on the corresponding quotient spaces $J$, are realizable as cubic polynomials on their (locally connected) Julia sets. In the present paper we use a new approach to construct cubic WT-laminations with all of the above properties and the extra property that the corresponding wandering branch point of $J$ has a dense orbit in each subarc of $J$ (we call such orbits \emph{condense}), and to show that critical portraits corresponding to such laminations are uncountably dense in the space $\A_3$ of all cubic critical portraits.

Affiliated with

Also associated with

No associations

Rating

Cubic Critical Portraits and Polynomials with Wandering Gaps 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 Cubic Critical Portraits and Polynomials with Wandering Gaps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cubic Critical Portraits and Polynomials with Wandering Gaps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-211830