Décroissance des corrélations pour un ensemble capté normalement hyperbolique
| Autor: | Maciej Zworski, Stéphane Nonnenmacher |
|---|---|
| Přispěvatelé: | Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Berkeley], University of California [Berkeley] (UC Berkeley), University of California (UC)-University of California (UC), DMS-1201417, University of California [Berkeley], University of California-University of California |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Polynomial
resonances General Mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] Semiclassical physics FOS: Physical sciences Dynamical Systems (math.DS) Resonance (particle physics) Mathematics - Analysis of PDEs spectral gap FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Mathematics - Dynamical Systems Mathematical Physics Mathematics hyperbolic set Geodesics in general relativity Mathematical analysis quantum scattering Mathematical Physics (math-ph) Flow (mathematics) Phase space Transversal (combinatorics) Symplectic geometry Analysis of PDEs (math.AP) |
| Zdroj: | Inventiones Mathematicae Inventiones Mathematicae, 2015, Inventiones Mathematicae, 200, pp.345-438. ⟨10.1007/s00222-014-0527-y⟩ Inventiones Mathematicae, Springer Verlag, 2015, Inventiones Mathematicae, 200, pp.345-438. ⟨10.1007/s00222-014-0527-y⟩ |
| ISSN: | 0020-9910 1432-1297 |
| DOI: | 10.1007/s00222-014-0527-y⟩ |
| Popis: | International audience; We prove that for evolution problems with normally hyperbolic trapping in phase space, correlations decay exponentially in time. Normal hyperbolic trapping means that the trapped set is smooth and symplectic and that the flow is hyperbolic in directions transversal to it. Flows with this structure include contact Anosov flows, classical flows in molecular dynamics, and null geodesic flows for black holes metrics. The decay of correlations is a consequence of the existence of resonance free strips for Green's functions (cut-off resolvents) and polynomial bounds on the growth sof those functions in the semiclassical parameter. |
| Databáze: | OpenAIRE |
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