Analytic and Probabilistic Approaches to Dynamics in Negative Curvature (eBook)

Françoise Dal'Bo, Marc Peigné, Andrea Sambusetti (Herausgeber)

eBook Download: PDF

2014 | 2014
XI, 138 Seiten
Springer International Publishing (Verlag)
978-3-319-04807-9 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 17.7.2014
• Reihe/Serie: Springer INdAM Series
• Reihe/Serie: Springer INdAM Series
• Zusatzinfo: XI, 138 p. 32 illus., 12 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik
• Schlagworte: Brownian motion • central limit theorem • Fuchsian group • Hyperbolic dynamics • ruelle-pollicott resonances
• ISBN-10: 3-319-04807-4 / 3319048074
• ISBN-13: 978-3-319-04807-9 / 9783319048079