Ergodic and Bernoulli properties of analytic maps of complex projective space

Author:
Lorelei Koss

Journal:
Trans. Amer. Math. Soc. **354** (2002), 2417-2459

MSC (2000):
Primary 37A25, 37A35, 37F10

DOI:
https://doi.org/10.1090/S0002-9947-02-02725-3

Published electronically:
February 7, 2002

MathSciNet review:
1885659

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Abstract: We examine the measurable ergodic theory of analytic maps of complex projective space. We focus on two different classes of maps, Ueda maps of , 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 ( ). We find analytic maps of and 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 , there exists a rational map of the sphere which is one-sided Bernoulli of entropy with respect to a smooth measure.

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Additional Information

**Lorelei Koss**

Affiliation:
Department of Mathematics and Computer Science, Dickinson College, P.O. Box 1773, Carlisle, Pennsylvania 17013

Email:
koss@dickinson.edu

DOI:
https://doi.org/10.1090/S0002-9947-02-02725-3

Received by editor(s):
March 22, 1999

Received by editor(s) in revised form:
March 14, 2000

Published electronically:
February 7, 2002

Additional Notes:
Supported in part by GAANN (Graduate Assistance in Areas of National Need) Fellowship

Article copyright:
© Copyright 2002
American Mathematical Society