LEADER 04417nam 22005653 450 001 9910915676103321 005 20231110214022.0 010 $a1-4704-7320-8 035 $a(MiAaPQ)EBC30330541 035 $a(Au-PeEL)EBL30330541 035 $a(CKB)25994202000041 035 $a(EXLCZ)9925994202000041 100 $a20230113d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Regularity of the Linear Drift in Negatively Curved Spaces 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2023. 210 4$dİ2023. 215 $a1 online resource (164 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.281 311 08$aPrint version: Ledrappier, François The Regularity of the Linear Drift in Negatively Curved Spaces Providence : American Mathematical Society,c2023 9781470455422 327 $aCover -- 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. 330 $a"We show that the linear drift of the Brownian motion on the universal cover of a closed connected smooth Riemannian manifold is Ck-2 differentiable along any Ck curve in the manifold of Ck Riemannian metrics with negative sectional curvature. We also show that the stochastic entropy of the Brownian motion is C1 differentiable along any C3 curve of C3 Riemannian metrics with negative sectional curvature. We formulate the first derivatives of the linear drift and stochastic entropy, respectively, and show they are critical at locally symmetric metrics"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aGeodesic flows 606 $aStochastic analysis 606 $aBrownian motion processes 606 $aDynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)$2msc 606 $aGlobal analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Diffusion processes and stochastic analysis on manifolds$2msc 615 0$aGeodesic flows. 615 0$aStochastic analysis. 615 0$aBrownian motion processes. 615 7$aDynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.). 615 7$aGlobal analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Diffusion processes and stochastic analysis on manifolds. 676 $a515/.39 676 $a516.352 686 $a37D40$a58J65$2msc 700 $aLedrappier$b François$0351144 701 $aShu$b Lin$01778426 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910915676103321 996 $aThe Regularity of the Linear Drift in Negatively Curved Spaces$94301278 997 $aUNINA LEADER 00984nas 2200385 c 450 001 9910133915403321 005 20171201144429.0 035 $a(CKB)3360000000446794 035 $a(OCoLC)682070011 035 $a(OCoLC)705915639 035 $a(DE-101)1007748109 035 $a(DE-599)ZDB2578162-5 035 $a(EXLCZ)993360000000446794 100 $a20101020a20109999 |y | 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aMedical case studies 210 31$aNairobi, Kenya$cAcademic Journals$d2010- 215 $aOnline-Ressource 300 $aGesehen am 20.10.10 311 08$a2141-6532 517 3 $aMed. Case Stud. 517 3 $aMCS 608 $aZeitschrift$2gnd-content 676 $a610 801 0$b0030 801 1$bDE-101 801 2$b9999 906 $aJOURNAL 912 $a9910133915403321 996 $aMedical case studies$92156249 997 $aUNINA