When do two rational functions have the same Julia set?

G. Levin*, And F. Przytycki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

It is proved that non-exceptional rational functions f and g on the Riemann sphere have the same measure of maximal entropy iff there exist iterates F of f and G of g and natural numbers M, N such that (*) (G-1 o G) o GM= (F-1 o F) o FN. If one assumes only that f, g have the same Julia set and no singular or parabolic domains of normality for the iterates, one also proves (*).

Original languageAmerican English
Pages (from-to)2179-2190
Number of pages12
JournalProceedings of the American Mathematical Society
Volume125
Issue number7
DOIs
StatePublished - 1997

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