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A one-stop introduction to the methods of ergodic theory applied to holomorphic iteration that is ideal for graduate courses.
Introduction
Basic examples and definitions
1. Measure preserving endomorphisms
2. Compact metric spaces
3. Distance expanding maps
4. Thermodynamical formalism
5. Expanding repellers in manifolds and in the Riemann sphere, preliminaries
6. Cantor repellers in the line, Sullivan's scaling function, application in Feigenbaum universality
7. Fractal dimensions
8. Conformal expanding repellers
9. Sullivan's classification of conformal expanding repellers
10. Holomorphic maps with invariant probability measures of positive Lyapunov exponent
11. Conformal measures
References
Index.
