An inequality for laminations, Julia sets and 'growing trees'

A. Blokh*, G. Levin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

For a closed lamination on the unit circle invariant under z → zd we prove an inequality relating the number of points in the 'gaps' with infinite pairwise disjoint orbits to the degree; in particular, this gives estimates on the cardinality of any such 'gap' as well as on the number of distinct grand orbits of such 'gaps'. As a tool, we introduce and study a dynamically defined growing tree in the quotient space. We also use our techniques to obtain for laminations an analog of Sullivan's no wandering domain theorem. Then we apply these results to Julia sets of polynomials.

Original languageAmerican English
Pages (from-to)63-97
Number of pages35
JournalErgodic Theory and Dynamical Systems
Volume22
Issue number1
DOIs
StatePublished - 2002

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