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)

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
Creator
Contributor
Editor
Provider
Subject
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 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
Member of
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)
Instantiates
Publication
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
10.1007/978-3-319-04807-9
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-04807-9
Label
Analytic and Probabilistic Approaches to Dynamics in Negative Curvature, edited by Françoise Dal'Bo, Marc Peigné, Andrea Sambusetti, (electronic resource)
Publication
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
10.1007/978-3-319-04807-9
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-04807-9

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