Topology and measure of buried points in Julia sets

• Autorzy: Clinton P. Curry , John C. Mayer , E. D. Tymchatyn
• Języki publikacji: EN

Abstrakty

EN

It is well-known that the set of buried points of a Julia set of a rational function (also called the residual Julia set) is topologically "fat" in the sense that it is a dense $G_{δ}$ if it is non-empty. We show that it is, in many cases, a full-measure subset of the Julia set with respect to conformal measure and the measure of maximal entropy. We also address Hausdorff dimension of buried points in the same cases, and discuss connectivity and topological dimension of the set of buried points. Finally, we present a non-dynamical example of a plane continuum whose set of buried points is a dense and hereditarily disconnected (components are points) $G_{δ}$, but not totally disconnected (not all quasi-components are points).

Kategorie tematyczne

• 54F50: Spaces of dimension ≤ 1 ; curves, dendrites
• 37F20: Combinatorics and topology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 222
• Numer: 1
• Strony: 1-17

Daty

wydano

2013

Twórcy

autor

Clinton P. Curry

• Department of Mathematics, Huntingdon College, Montgomery, AL 36106, U.S.A.

autor

John C. Mayer

• Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170, U.S.A.

autor

E. D. Tymchatyn

• Department of Mathematics, University of Saskatchewan, Saskatoon, SK, S7N 5E6, Canada

Identyfikatory

DOI

10.4064/fm222-1-1