Analytic and Probabilistic Approaches to Dynamics in Negative Curvature: Springer INdAM Series, cartea 9
Editat de Françoise Dal'Bo, Marc Peigné, Andrea Sambusettien Limba Engleză Hardback – aug 2014
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Specificații
ISBN-13: 9783319048062
ISBN-10: 3319048066
Pagini: 149
Ilustrații: XI, 138 p. 32 illus., 12 illus. in color.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.39 kg
Ediția:2014
Editura: Springer International Publishing
Colecția Springer
Seria Springer INdAM Series
Locul publicării:Cham, Switzerland
ISBN-10: 3319048066
Pagini: 149
Ilustrații: XI, 138 p. 32 illus., 12 illus. in color.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.39 kg
Ediția:2014
Editura: Springer International Publishing
Colecția Springer
Seria Springer INdAM Series
Locul publicării:Cham, Switzerland
Public țintă
ResearchCuprins
1 S. Le Borgne: Martingales in Hyperbolic Geometry.- 2 F. Faure, M. Tsujii: Semi classical Approach for the Ruelle-Pollicott Spectrum of Hyperbolic Dynamics.
Textul de pe ultima copertă
The work of E. Hopf and G.A. Hedlund, in the 1930s, on transitivity and ergodicity of the geodesic flow for hyperbolic surfaces, marked the beginning of the investigation of the statistical properties and stochastic behavior of the flow. The first central limit theorem for the geodesic flow was proved in the 1960s by Y. Sinai for compact hyperbolic manifolds. Since then, strong relationships have been found between the fields of ergodic theory, analysis, and geometry. Different approaches and new tools have been developed to study the geodesic flow, including measure theory, thermodynamic formalism, transfer operators, Laplace operators, and Brownian motion. All these different points of view have led to a deep understanding of more general dynamical systems, in particular the so-called Anosov systems, with applications to geometric problems such as counting, equirepartition, mixing, and recurrence properties of the orbits.
This book comprises two independent texts that provide a self-contained introduction to two different approaches to the investigation of hyperbolic dynamics. The first text, by S. Le Borgne, explains the method of martingales for the central limit theorem. This approach can be used in several situations, even for weakly hyperbolic flows, and the author presents a good number of examples and applications to equirepartition and mixing. The second text, by F. Faure and M. Tsujii, concerns the semiclassical approach, by operator theory: chaotic dynamics is described through the spectrum of the associated transfer operator, with applications to the asymptotic counting of periodic orbits.
The book will be of interest for a broad audience, from PhD and Post-Doc students to experts working on geometry and dynamics.
This book comprises two independent texts that provide a self-contained introduction to two different approaches to the investigation of hyperbolic dynamics. The first text, by S. Le Borgne, explains the method of martingales for the central limit theorem. This approach can be used in several situations, even for weakly hyperbolic flows, and the author presents a good number of examples and applications to equirepartition and mixing. The second text, by F. Faure and M. Tsujii, concerns the semiclassical approach, by operator theory: chaotic dynamics is described through the spectrum of the associated transfer operator, with applications to the asymptotic counting of periodic orbits.
The book will be of interest for a broad audience, from PhD and Post-Doc students to experts working on geometry and dynamics.
Caracteristici
Quick and mostly self-contained introduction to problems and methods Exposition stays as elementary as possible with key-examples Interesting to mathematicians working on geometry, dynamics, probability, operators theory Includes supplementary material: sn.pub/extras