Analytic and Probabilistic Approaches to Dynamics in Negative Curvature

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

Buch | Softcover

XI, 138 Seiten

2016 | Softcover reprint of the original 1st ed. 2014
Springer International Publishing (Verlag)
978-3-319-38117-6 (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.

Erscheinungsdatum	29.08.2016
Reihe/Serie	Springer INdAM Series
Zusatzinfo	XI, 138 p. 32 illus., 12 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Brownian motion • central limit theorem • Differential and Riemannian geometry • Differential Geometry • Dynamical Systems and Ergodic Theory • Fuchsian group • Functional analysis and transforms • Hyperbolic dynamics • Hyperbolic Geometry • mathematics and statistics • Non-Euclidean geometry • Nonlinear Science • operator theory • probability and statistics • Probability theory and stochastic processes • ruelle-pollicott resonances • stochastics
ISBN-10	3-319-38117-2 / 3319381172
ISBN-13	978-3-319-38117-6 / 9783319381176
Zustand	Neuware