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Conformal and harmonic measures on laminations associated with rational maps / / Vadim A. Kaimanovich, Mikhail Lyubich
| Conformal and harmonic measures on laminations associated with rational maps / / Vadim A. Kaimanovich, Mikhail Lyubich |
| Autore | Kaimanovich Vadim A. |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2005 |
| Descrizione fisica | 1 online resource (134 p.) |
| Disciplina |
510 s
515/.9 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Conformal mapping
Geometry, Hyperbolic Measure theory Differential topology Complex manifolds Hyperbolic spaces Kleinian groups |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0421-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910480533903321 |
Kaimanovich Vadim A.
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Conformal and harmonic measures on laminations associated with rational maps / / Vadim A. Kaimanovich, Mikhail Lyubich
| Conformal and harmonic measures on laminations associated with rational maps / / Vadim A. Kaimanovich, Mikhail Lyubich |
| Autore | Kaimanovich Vadim A. |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2005 |
| Descrizione fisica | 1 online resource (134 p.) |
| Disciplina |
510 s
515/.9 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Conformal mapping
Geometry, Hyperbolic Measure theory Differential topology Complex manifolds Hyperbolic spaces Kleinian groups |
| ISBN | 1-4704-0421-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910788748703321 |
|
Kaimanovich Vadim A.
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Conformal and harmonic measures on laminations associated with rational maps / / Vadim A. Kaimanovich, Mikhail Lyubich
| Conformal and harmonic measures on laminations associated with rational maps / / Vadim A. Kaimanovich, Mikhail Lyubich |
| Autore | Kaimanovich Vadim A. |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2005 |
| Descrizione fisica | 1 online resource (134 p.) |
| Disciplina |
510 s
515/.9 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Conformal mapping
Geometry, Hyperbolic Measure theory Differential topology Complex manifolds Hyperbolic spaces Kleinian groups |
| ISBN | 1-4704-0421-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910812425703321 |
|
Kaimanovich Vadim A.
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Laminations and foliations in dynamics, geometry and topology : proceedings of the Conference on Laminations and Foliations in Dynamics, Geometry and Topology, May 18-24, 1998, SUNY at Stony Brook / / Mikhail Lyubich, John W. Milnor, Yair N. Minsky, editors
| Laminations and foliations in dynamics, geometry and topology : proceedings of the Conference on Laminations and Foliations in Dynamics, Geometry and Topology, May 18-24, 1998, SUNY at Stony Brook / / Mikhail Lyubich, John W. Milnor, Yair N. Minsky, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2001] |
| Descrizione fisica | 1 online resource (250 p.) |
| Disciplina | 514/.72 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Foliations (Mathematics)
Geometry, Differential |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-8218-7859-X
0-8218-5605-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Geodesic laminations on surfaces""; ""Part I. The dynamical viewpoint""; ""Definitions and first properties""; ""Examples of geodesic laminations""; ""The topology of geodesic laminations""; ""The higher dimensional case""; ""A more explicit example""; ""Local properties of geodesic laminations""; ""Transverse structures""; ""Part II. The topological viewpoint""; ""The topology and piecewise linear structure of ML(S)""; ""Change of metric""; ""The length function""; ""Tangent vectors to ML(S)""; ""The derivative of the length function""
""Part III. The geometric viewpoint""""The convex core of a hyperbolic 3â€?manifold""; ""Pleated surfaces in hyperbolic 3â€?manifolds""; ""Variations of the geometry of convex cores""; ""Rotation angles, bending cocycles and Thurston's intersection form""; ""References""; ""Index""; ""Dicritical singularities of holomorphic vector fields""; ""Dynamics of P2 (Examples)""; ""1. Introduction""; ""2. Attractors""; ""2.1 Trapping region""; ""2.2 The map Î?""; ""2.3 Non-Algebraicity of A""; ""2.4 Subhyperbolicity of attractors"" ""3. When the compact set of points with bounded orbit is disjoint from the critical set""""3.1 J = P2""; ""3.2 Support of Î?""; ""4. Isolated repelling points""; ""4.1 Isolated repelling orbits""; ""4.2 The compact set K of points with bounded orbit""; ""5. Examples of endomorphisms such that Supp Î? = Julia set""; ""3 lectures on foliations and laminations on 3-manifolds""; ""Rational laminations of complex polynomials""; ""Actions of discrete groups on complex projective spaces""; ""Dynamics of singular holomorphic foliations on the complex projective plane""; ""Preface""; ""Introduction"" ""1. Singular Holomorphic Foliations by Curves""""2. The Monodromy Group of a Leaf""; ""3. Density and Ergodicity Theorems""; ""4. Non-Trivial Minimal Sets""; ""References"" |
| Record Nr. | UNINA-9910480309303321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2001] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Laminations and foliations in dynamics, geometry and topology : proceedings of the Conference on Laminations and Foliations in Dynamics, Geometry and Topology, May 18-24, 1998, SUNY at Stony Brook / / Mikhail Lyubich, John W. Milnor, Yair N. Minsky, editors
| Laminations and foliations in dynamics, geometry and topology : proceedings of the Conference on Laminations and Foliations in Dynamics, Geometry and Topology, May 18-24, 1998, SUNY at Stony Brook / / Mikhail Lyubich, John W. Milnor, Yair N. Minsky, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2001] |
| Descrizione fisica | 1 online resource (250 p.) |
| Disciplina | 514/.72 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Foliations (Mathematics)
Geometry, Differential |
| ISBN |
0-8218-7859-X
0-8218-5605-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Geodesic laminations on surfaces""; ""Part I. The dynamical viewpoint""; ""Definitions and first properties""; ""Examples of geodesic laminations""; ""The topology of geodesic laminations""; ""The higher dimensional case""; ""A more explicit example""; ""Local properties of geodesic laminations""; ""Transverse structures""; ""Part II. The topological viewpoint""; ""The topology and piecewise linear structure of ML(S)""; ""Change of metric""; ""The length function""; ""Tangent vectors to ML(S)""; ""The derivative of the length function""
""Part III. The geometric viewpoint""""The convex core of a hyperbolic 3â€?manifold""; ""Pleated surfaces in hyperbolic 3â€?manifolds""; ""Variations of the geometry of convex cores""; ""Rotation angles, bending cocycles and Thurston's intersection form""; ""References""; ""Index""; ""Dicritical singularities of holomorphic vector fields""; ""Dynamics of P2 (Examples)""; ""1. Introduction""; ""2. Attractors""; ""2.1 Trapping region""; ""2.2 The map Î?""; ""2.3 Non-Algebraicity of A""; ""2.4 Subhyperbolicity of attractors"" ""3. When the compact set of points with bounded orbit is disjoint from the critical set""""3.1 J = P2""; ""3.2 Support of Î?""; ""4. Isolated repelling points""; ""4.1 Isolated repelling orbits""; ""4.2 The compact set K of points with bounded orbit""; ""5. Examples of endomorphisms such that Supp Î? = Julia set""; ""3 lectures on foliations and laminations on 3-manifolds""; ""Rational laminations of complex polynomials""; ""Actions of discrete groups on complex projective spaces""; ""Dynamics of singular holomorphic foliations on the complex projective plane""; ""Preface""; ""Introduction"" ""1. Singular Holomorphic Foliations by Curves""""2. The Monodromy Group of a Leaf""; ""3. Density and Ergodicity Theorems""; ""4. Non-Trivial Minimal Sets""; ""References"" |
| Record Nr. | UNINA-9910788654603321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2001] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Laminations and foliations in dynamics, geometry and topology : proceedings of the Conference on Laminations and Foliations in Dynamics, Geometry and Topology, May 18-24, 1998, SUNY at Stony Brook / / Mikhail Lyubich, John W. Milnor, Yair N. Minsky, editors
| Laminations and foliations in dynamics, geometry and topology : proceedings of the Conference on Laminations and Foliations in Dynamics, Geometry and Topology, May 18-24, 1998, SUNY at Stony Brook / / Mikhail Lyubich, John W. Milnor, Yair N. Minsky, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2001] |
| Descrizione fisica | 1 online resource (250 p.) |
| Disciplina | 514/.72 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Foliations (Mathematics)
Geometry, Differential |
| ISBN |
0-8218-7859-X
0-8218-5605-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Geodesic laminations on surfaces""; ""Part I. The dynamical viewpoint""; ""Definitions and first properties""; ""Examples of geodesic laminations""; ""The topology of geodesic laminations""; ""The higher dimensional case""; ""A more explicit example""; ""Local properties of geodesic laminations""; ""Transverse structures""; ""Part II. The topological viewpoint""; ""The topology and piecewise linear structure of ML(S)""; ""Change of metric""; ""The length function""; ""Tangent vectors to ML(S)""; ""The derivative of the length function""
""Part III. The geometric viewpoint""""The convex core of a hyperbolic 3â€?manifold""; ""Pleated surfaces in hyperbolic 3â€?manifolds""; ""Variations of the geometry of convex cores""; ""Rotation angles, bending cocycles and Thurston's intersection form""; ""References""; ""Index""; ""Dicritical singularities of holomorphic vector fields""; ""Dynamics of P2 (Examples)""; ""1. Introduction""; ""2. Attractors""; ""2.1 Trapping region""; ""2.2 The map Î?""; ""2.3 Non-Algebraicity of A""; ""2.4 Subhyperbolicity of attractors"" ""3. When the compact set of points with bounded orbit is disjoint from the critical set""""3.1 J = P2""; ""3.2 Support of Î?""; ""4. Isolated repelling points""; ""4.1 Isolated repelling orbits""; ""4.2 The compact set K of points with bounded orbit""; ""5. Examples of endomorphisms such that Supp Î? = Julia set""; ""3 lectures on foliations and laminations on 3-manifolds""; ""Rational laminations of complex polynomials""; ""Actions of discrete groups on complex projective spaces""; ""Dynamics of singular holomorphic foliations on the complex projective plane""; ""Preface""; ""Introduction"" ""1. Singular Holomorphic Foliations by Curves""""2. The Monodromy Group of a Leaf""; ""3. Density and Ergodicity Theorems""; ""4. Non-Trivial Minimal Sets""; ""References"" |
| Record Nr. | UNINA-9910828839403321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2001] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||