The Regularity of the Linear Drift in Negatively Curved Spaces

• Autore: Ledrappier François
• Pubblicazione: Providence : , : American Mathematical Society, , 2023; ©2023
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (164 pages)
• Disciplina: 515/.39; 516.352
• Soggetto topico: Geodesic flows; Stochastic analysis; Brownian motion processes; Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.); Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Diffusion processes and stochastic analysis on manifolds
• Classificazione: 37D4058J65
• Altri autori: ShuLin
• Nota di contenuto: Cover -- Title page -- Chapter 1. Introduction and statement of results -- Main notations and conventions -- Chapter 2. Preliminaries -- 2.1. Jacobi fields and the geodesic flow -- 2.2. Anosov flow and invariant manifolds -- 2.3. Harmonic measure for the stable foliation -- 2.4. Busemann function and the linear drift -- Chapter 3. Regularity of the linear drift -- 3.1. Regularity of the leafwise divergence term ^{ }\overline{ } -- 3.2. Regularity of the harmonic measure -- 3.3. Differentials of the linear drift -- Chapter 4. Brownian motion and stochastic flows -- 4.1. Parallelism and the Brownian motion -- 4.2. A stochastic analogue of the geodesic flow -- 4.3. Growth of the stochastic tangent maps in time -- 4.4. Brownian bridge and conditional estimations -- 4.5. Regularity of the stochastic analogue of the geodesic flow -- Chapter 5. The first differential of the heat kernels in metrics -- 5.1. Strategy -- 5.2. A description of _{ }^{ } -- 5.3. The existence of ^{ }_{ } -- 5.4. Quasi-invariance property of _{ }^{ } -- 5.5. The extended map ^{ } -- 5.6. The differential of \mapsto ^{ }( , ,⋅) -- Chapter 6. Higher order regularity of the heat kernels in metrics -- 6.1. A sketch of the proof for Theorem 1.3 with ≥2 -- 6.2. Proofs of the properties concerning ^{ }_{ } -- Chapter 7. Regularity of the stochastic entropy -- Acknowledgments -- Bibliography -- Back Cover.
• Sommario/riassunto: "We show that the linear drift of the Brownian motion on the universal cover of a closed connected smooth Riemannian manifold is Ck-2 differentiable along any Ck curve in the manifold of Ck Riemannian metrics with negative sectional curvature. We also show that the stochastic entropy of the Brownian motion is C1 differentiable along any C3 curve of C3 Riemannian metrics with negative sectional curvature. We formulate the first derivatives of the linear drift and stochastic entropy, respectively, and show they are critical at locally symmetric metrics"--
• Titolo autorizzato: The Regularity of the Linear Drift in Negatively Curved Spaces
• ISBN: 1-4704-7320-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910915676103321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society