1.

Record Nr.

UNINA9910480533903321

Autore

Kaimanovich Vadim A.

Titolo

Conformal and harmonic measures on laminations associated with rational maps / / Vadim A. Kaimanovich, Mikhail Lyubich

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , 2005

©2005

ISBN

1-4704-0421-4

Descrizione fisica

1 online resource (134 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 820

Disciplina

510 s

515/.9

Soggetti

Conformal mapping

Geometry, Hyperbolic

Measure theory

Differential topology

Complex manifolds

Hyperbolic spaces

Kleinian groups

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"Volume 173, number 820 (end of volume)."

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

""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""