Conformal and Harmonic Measures on Laminations Associated with Rational Maps.

Intro -- Contents -- Introduction -- Chapter 1. Affine and hyperbolic laminations -- 1.1. Afflne plane and hyperbolic space -- 1.2. The notion of lamination -- 1.3. Cohomology of an affine lamination -- Chapter 2. Measures and currents on laminations -- 2.1. Measures on general laminations -- 2.2. Measures and streams on affine and hyperbolic laminations -- 2.3. Conformal streams, harmonic measures and harmonic functions -- 2.4. Measures and streams on quotient laminations -- Chapter 3. Laminations associated with rational maps -- 3.1. Construction of the affine lamination -- 3.2. The Busemann and basic cocycles of a rational map -- 3.3. An example of a special section -- 3.4. Dual basic cocycle -- 3.5. Euclidean laminations -- Chapter 4. Measures on laminations associated with rational maps -- 4.1. The balanced measures -- 4.2. Equidistribution of leaves -- 4.3. Critical exponent -- 4.4. Transverse conformal stream and λ-harmonic measure -- 4.5. Leafwise conformal streams -- 4.6. Sullivan's Riemann surface laminations -- 4.7. Problems -- Appendix A. Laminations associated with Kleinian groups -- A.1. Foliations associated with the hyperbolic space -- A.2. Laminations associated with Kleinian groups -- A.3. Metrics on the Riemann sphere -- A.4. Conformal streams and invariant measures of the geodesic flow -- A.5. New lines in the dictionary -- A.6. An example of a non-Euclidean affine foliation -- List of notations -- Bibliography.

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