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Analytic and Probabilistic Approaches to Dynamics in Negative Curvature (Hardcover, 2014 ed.)
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Analytic and Probabilistic Approaches to Dynamics in Negative Curvature (Hardcover, 2014 ed.)
Series: Springer INdAM Series, 9
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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 Stephane Le Borgne);the semi-classical approach, by
operator theory and resonances (by Frederic 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."
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