| EAN: | 9783319048062 |
|---|---|
| Sachgruppe: | Mathematik |
| Sprache: | Englisch |
| Seitenzahl: | 152 |
| Produktart: | Gebunden |
| Herausgeber: | Dal'Bo, Françoise Peigné, Marc Sambusetti, Andrea |
| Veröffentlichungsdatum: | 01.08.2014 |
| Schlagworte: | Differenzialgeometrie Geometrie / Differenzialgeometrie Wahrscheinlichkeit - Wahrscheinlichkeitstheorie |
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The work consists of two introductory courses, developing different points of view on the study of the asymptotic behaviour of the geodesic flow, namely: the probabilistic approach via martingales and mixing (by Stéphane Le Borgne); the semi-classical approach, by operator theory and resonances (by Frédéric Faure and Masato Tsujii). The contributions aim to give a self-contained introduction to the ideas behind the three different approaches to the investigation of hyperbolic dynamics. The first contribution focus on the convergence towards a Gaussian law of suitably normalized ergodic sums (Central Limit Theorem). The second one deals with Transfer Operators and the structure of their spectrum (Ruelle-Pollicott resonances), explaining the relation with the asymptotics of time correlation function and the periodic orbits of the dynamics.
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