Analytic and Probabilistic Approaches to Dynamics in Negative Curvature

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Juli 2014



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.


1 S. Le Borgne: Martingales in Hyperbolic Geometry.- 2 F. Faure, M. Tsujii: Semi classical Approach for the Ruelle-Pollicott Spectrum of Hyperbolic Dynamics.


EAN: 9783319048062
ISBN: 3319048066
Untertitel: 'Springer INdAM Series'. 2014. 2014. 20 schwarz-weiße und 12 farbige Abbildungen, Bibliographie. Book. Sprache: Englisch.
Verlag: Springer-Verlag GmbH
Erscheinungsdatum: Juli 2014
Seitenanzahl: XI
Format: gebunden
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