Jordan tori and polynomial endomorphisms in ℂ2

Manfred Heinz Denker, Stefan M. Heinemann

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

For a class of quadratic polynomial endomorphisms f : ℂ2 → ℂ2 close to the standard torus map (x, y) → (x2, y2), we show that the Julia set J(f) is homeomorphic to the torus. We identify J(f) as the closure ℛ of the set of repelling periodic points and as the Shilov boundary of the set K(f) of points with bounded forward orbit. Moreover, it turns out that (J(f),f) is a mixing repeller and supports a measure of maximal entropy for f which is uniquely determined as the harmonic measure for K(f).

Original languageEnglish (US)
Pages (from-to)139-159
Number of pages21
JournalFundamenta Mathematicae
Volume157
Issue number2-3
StatePublished - 1998

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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