Absolutely Continuous Invariant Measures for Expansive Rational Maps with Rationally Indifferent Periodic Points

Manfred Heinz Denker, Mariusz Urbanski

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Abstract

Expansive rational maps T:C→ C which are not expanding with respect to the spherical metric are those which have rationally indifferent periodic points. For an atomless t-conformal measure m of such a rational map we prove the existence of a unique (up to a multiplicative constant) σ-finite, T-invariant measureμabsolutely continuous with respect to m. We also give a necessary and sufficient condition for the measureμ to be finite.

Original languageEnglish (US)
Pages (from-to)561-580
Number of pages20
JournalForum Mathematicum
Volume3
Issue number3
DOIs
Publication statusPublished - Jan 1 1991

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Denker, Manfred Heinz ; Urbanski, Mariusz. / Absolutely Continuous Invariant Measures for Expansive Rational Maps with Rationally Indifferent Periodic Points. In: Forum Mathematicum. 1991 ; Vol. 3, No. 3. pp. 561-580.