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

Manfred Denker; Mariusz Urbanski

doi:10.1515/form.1991.3.561

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

Manfred Denker, Mariusz Urbanski

Mathematics

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

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 language	English (US)
Pages (from-to)	561-580
Number of pages	20
Journal	Forum Mathematicum
Volume	3
Issue number	3
DOIs	https://doi.org/10.1515/form.1991.3.561
State	Published - Jan 1 1991

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1515/form.1991.3.561

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