Title

Ergodic and Bernoulli Properties of Analytic Maps of Complex Projective Space

Document Type

Article

Publication Date

2-7-2002

Department

Mathematics

Language

English

Publication Title

Transactions of the American Mathematical Society

Abstract

We examine the measurable ergodic theory of analytic maps F of complex projective space. We focus on two different classes of maps, Ueda maps of Pn, and rational maps of the sphere with parabolic orbifold and Julia set equal to the entire sphere. We construct measures which are invariant, ergodic, weak- or strong-mixing, exact, or automorphically Bernoulli with respect to these maps. We discuss topological pressure and measures of maximal entropy (hµ(F) = htop(F) = log(deg F)). We find analytic maps of P1 and P2 which are one-sided Bernoulli of maximal entropy, including examples where the maximal entropy measure lies in the smooth measure class. Further, we prove that for any integer d > 1, there exists a rational map of the sphere which is one-sided Bernoulli of entropy log d with respect to a smooth measure.

Comments

Published as:
Koss, Lorelei. "Ergodic and Bernoulli Properties of Analytic Maps of Complex Projective Space." Transactions of the American Mathematical Society 354, no. 6 (2002): 2417-2459.

For more information on the published version, visit American Mathematical Society's Website.

DOI

10.1090/S0002-9947-02-02725-3

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