Description
Analytic and Probabilistic Approaches to Dynamics in Negative Curvature, Softcover reprint of the original 1st ed. 2014
Springer INdAM Series, Vol. 9
Coordinators: Dal'Bo Françoise, Peigné Marc, Sambusetti Andrea
Language: EnglishSubject for Analytic and Probabilistic Approaches to Dynamics in...:
Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
Publication date: 08-2016
Support: Print on demand
Publication date: 08-2016
Support: Print on demand
Geometric, Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
Publication date: 08-2014
138 p. · 15.5x23.5 cm · Hardback
Publication date: 08-2014
138 p. · 15.5x23.5 cm · Hardback
Description
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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.
1 S. Le Borgne: Martingales in Hyperbolic Geometry.- 2 F. Faure, M. Tsujii: Semi classical Approach for the Ruelle-Pollicott Spectrum of Hyperbolic Dynamics.
Quick and mostly self-contained introduction to problems and methods Exposition stays as elementary as possible with key-examples Interesting to mathematicians working on geometry, dynamics, probability, operators theory Includes supplementary material: sn.pub/extras
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