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Analytic and Probabilistic Approaches to Dynamics in Negative Curvature

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

Buch | Hardcover

XI, 138 Seiten

2014
Springer International Publishing (Verlag)
978-3-319-04806-2 (ISBN)

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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.

Erscheint lt. Verlag	1.8.2014
Reihe/Serie	Springer INdAM Series
Zusatzinfo	XI, 138 p. 32 illus., 12 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	397 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Brownian motion • central limit theorem • Fuchsian group • Hyperbolic dynamics • ruelle-pollicott resonances
ISBN-10	3-319-04806-6 / 3319048066
ISBN-13	978-3-319-04806-2 / 9783319048062
Zustand	Neuware