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The Resource Analytic and Probabilistic Approaches to Dynamics in Negative Curvature, edited by Françoise Dal'Bo, Marc Peigné, Andrea Sambusetti, (electronic resource)
Analytic and Probabilistic Approaches to Dynamics in Negative Curvature, edited by Françoise Dal'Bo, Marc Peigné, Andrea Sambusetti, (electronic resource)
Resource Information
The item Analytic and Probabilistic Approaches to Dynamics in Negative Curvature, edited by Françoise Dal'Bo, Marc Peigné, Andrea Sambusetti, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Analytic and Probabilistic Approaches to Dynamics in Negative Curvature, edited by Françoise Dal'Bo, Marc Peigné, Andrea Sambusetti, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 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 socalled 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 selfcontained 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 PostDoc students to experts working on geometry and dynamics
 Language
 eng
 Extent
 XI, 138 p. 32 illus., 12 illus. in color.
 Isbn
 9783319048079
 Label
 Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
 Title
 Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
 Statement of responsibility
 edited by Françoise Dal'Bo, Marc Peigné, Andrea Sambusetti
 Subject

 Global differential geometry
 Operator theory
 Distribution (Probability theory)
 Probability Theory and Stochastic Processes
 Operator Theory
 Global differential geometry
 Differentiable dynamical systems
 Distribution (Probability theory)
 Electronic resources
 Operator Theory
 Mathematics
 Differential Geometry
 Mathematics
 Differentiable dynamical systems
 Dynamical Systems and Ergodic Theory
 Hyperbolic Geometry
 Distribution (Probability theory)
 Operator theory
 Language
 eng
 Summary
 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 socalled 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 selfcontained 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 PostDoc students to experts working on geometry and dynamics
 http://library.link/vocab/creatorName
 Dal'Bo, Françoise
 Image bit depth
 0
 LC call number
 QA313
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Peigné, Marc.
 Sambusetti, Andrea.
 SpringerLink
 Series statement
 Springer INdAM Series,
 Series volume
 9
 http://library.link/vocab/subjectName

 Mathematics
 Differentiable dynamical systems
 Operator theory
 Global differential geometry
 Distribution (Probability theory)
 Mathematics
 Dynamical Systems and Ergodic Theory
 Probability Theory and Stochastic Processes
 Operator Theory
 Hyperbolic Geometry
 Differential Geometry
 Label
 Analytic and Probabilistic Approaches to Dynamics in Negative Curvature, edited by Françoise Dal'Bo, Marc Peigné, Andrea Sambusetti, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Dimensions
 unknown
 Extent
 XI, 138 p. 32 illus., 12 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319048079
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319048079
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319048079
 Label
 Analytic and Probabilistic Approaches to Dynamics in Negative Curvature, edited by Françoise Dal'Bo, Marc Peigné, Andrea Sambusetti, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Dimensions
 unknown
 Extent
 XI, 138 p. 32 illus., 12 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319048079
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319048079
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319048079
Subject
 Differentiable dynamical systems
 Differentiable dynamical systems
 Differential Geometry
 Distribution (Probability theory)
 Distribution (Probability theory)
 Distribution (Probability theory)
 Dynamical Systems and Ergodic Theory
 Electronic resources
 Global differential geometry
 Global differential geometry
 Hyperbolic Geometry
 Mathematics
 Mathematics
 Operator Theory
 Operator Theory
 Operator theory
 Operator theory
 Probability Theory and Stochastic Processes
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