03689nam 2200709 450 991048053390332120170816143327.01-4704-0421-4(CKB)3360000000465004(EBL)3114212(SSID)ssj0000973324(PQKBManifestationID)11553110(PQKBTitleCode)TC0000973324(PQKBWorkID)10959568(PQKB)11302693(MiAaPQ)EBC3114212(PPN)195417089(EXLCZ)99336000000046500420040903h20052005 uy| 0engur|n|---|||||txtccrConformal and harmonic measures on laminations associated with rational maps /Vadim A. Kaimanovich, Mikhail LyubichProvidence, Rhode Island :American Mathematical Society,2005.©20051 online resource (134 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 820"Volume 173, number 820 (end of volume)."0-8218-3615-3 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;no. 820.Conformal mappingGeometry, HyperbolicMeasure theoryDifferential topologyComplex manifoldsHyperbolic spacesKleinian groupsElectronic books.Conformal mapping.Geometry, Hyperbolic.Measure theory.Differential topology.Complex manifolds.Hyperbolic spaces.Kleinian groups.510 s515/.9Kaimanovich Vadim A.898963Lyubich Mikhail1959-MiAaPQMiAaPQMiAaPQBOOK9910480533903321Conformal and harmonic measures on laminations associated with rational maps2008388UNINA