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.
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Illustrationen
20 s/w Abbildungen, 12 farbige Abbildungen
XI, 138 p. 32 illus., 12 illus. in color.
Dateigröße
ISBN-13
978-3-319-04807-9 (9783319048079)
DOI
10.1007/978-3-319-04807-9
Schweitzer Klassifikation
1 S. Le Borgne: Martingales in Hyperbolic Geometry.- 2 F. Faure, M. Tsujii: Semi classical Approach for the Ruelle-Pollicott Spectrum of Hyperbolic Dynamics.
