Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
Seiten
2014
|
2014
Springer International Publishing (Verlag)
978-3-319-04806-2 (ISBN)
Springer International Publishing (Verlag)
978-3-319-04806-2 (ISBN)
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 |
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 |
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