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The Resource Aspects of ergodic, qualitative, and statistical theory of motion, G. Gallavotti, F. Bonetto, G. Gentile

Aspects of ergodic, qualitative, and statistical theory of motion, G. Gallavotti, F. Bonetto, G. Gentile

Work
Publication
Extent
x, 435 pages
Contents
  • 1. General qualitative properties
  • 1.1. Historical note
  • 1.2. Examples and some definitions
  • 1.3. Harmonic oscillators and integrable systems as dynamical systems
  • 1.4. Frequencies of visit
  • 2. Ergodicity and ergodic points
  • 2.1. Quasi-periodic motions and integrability
  • 2.2. Ergodic properties of quasi-periodic motions; Ergodic sequences and measures
  • 2.3. Ergodic points
  • 2.4. Ergodic decomposition
  • 3. Entropy and complexity
  • 3.1. Complexity of motions and entropy
  • 3.2. The Shannon-McMillan theorem
  • 3.3. Elementary properties of the average entropy
  • 3.4. Further properties of the average entropy; Generator theorem
  • 4. Markovian pavements
  • 4.1. Compatibility of histories; Markovian pavements
  • 4.2. Markovian pavements for hyperbolic systems
  • 4.3. Coding of the volume measure of smooth hyperbolic systems
  • 5. Gibbs distributions
  • 5.1. Gibbs distributions
  • 5.2. Properties of Gibbs distributions
  • 5.3. Gibbs distributions on Z+
  • 5.4. An application: Expansive maps of [0,1]
  • 6. General properties of Gibbs and SRB distributions
  • 6.1. Variational properties of Gibbs distributions
  • 6.2. Applications to Ansov systems; SRB distribution
  • 6.3. Periodic orbits, invariant probability distributions and entropy
  • 6.4. Equivalent potentials; Gibbs distributions with transitive vacuum
  • 7. Analyticity, singularity and phase transitions
  • 7.1. Polymers
  • 7.2. Cluster expansions
  • 7.3. Renormalization by decimation in one-dimensional systems
  • 7.4. Absence of phase transitions: More criteria
  • 7.5. Phase transitions
  • 8. Special ergodic theory problems in nonchaotic dynamics
  • 8.1. Theory of quasi-periodic Hamiltonian motions
  • 8.2 Graphs and diagrams for the Lindstedt series
  • 8.3. Cancellations
  • 8.4. Convergence and the KAM theorem
  • 9. Some special topics in KAM theory
  • 9.1. Resummations and renormalized series for invariant tori
  • 9.2. Bounds on renormalized series; Convergence
  • 9.3. Scaling laws for the standard map
  • 9.4. Limit function for the standard map near resonances
  • 10. Special problems in chaotic dynamics
  • 10.1. Perturbing Arnold's cat map
  • 10.2. Extending systems; Lattices of Arnold's cat maps
  • 10.3. Chaos in time: An SRB distribution
  • 10.4. Chaos in space-time and SRB distributions
  • 10.5. Isomorphisms
  • Appendix A: Nonequilibrium thermodynamics? Twenty-seven comments
Isbn
9783540408796
Instance
Label
Aspects of ergodic, qualitative, and statistical theory of motion
Title
Aspects of ergodic, qualitative, and statistical theory of motion
Statement of responsibility
G. Gallavotti, F. Bonetto, G. Gentile
Creator
Contributor
Subject
Language
  • eng
  • ita
  • eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Gallavotti, Giovanni
Dewey number
515/.48
Illustrations
illustrations
Index
index present
LC call number
QA313
LC item number
.G3516 2004
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Bonetto, F.
  • Gentile, G.
Series statement
Texts and monographs in physics,
http://library.link/vocab/subjectName
  • Ergodic theory
  • Measure-preserving transformations
  • Statistical mechanics
  • Differentiable dynamical systems
Label
Aspects of ergodic, qualitative, and statistical theory of motion, G. Gallavotti, F. Bonetto, G. Gentile
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages [411]-421) and indexes
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1. General qualitative properties -- 1.1. Historical note -- 1.2. Examples and some definitions -- 1.3. Harmonic oscillators and integrable systems as dynamical systems -- 1.4. Frequencies of visit -- 2. Ergodicity and ergodic points -- 2.1. Quasi-periodic motions and integrability -- 2.2. Ergodic properties of quasi-periodic motions; Ergodic sequences and measures -- 2.3. Ergodic points -- 2.4. Ergodic decomposition -- 3. Entropy and complexity -- 3.1. Complexity of motions and entropy -- 3.2. The Shannon-McMillan theorem -- 3.3. Elementary properties of the average entropy -- 3.4. Further properties of the average entropy; Generator theorem -- 4. Markovian pavements -- 4.1. Compatibility of histories; Markovian pavements -- 4.2. Markovian pavements for hyperbolic systems -- 4.3. Coding of the volume measure of smooth hyperbolic systems -- 5. Gibbs distributions -- 5.1. Gibbs distributions -- 5.2. Properties of Gibbs distributions -- 5.3. Gibbs distributions on Z+ -- 5.4. An application: Expansive maps of [0,1] -- 6. General properties of Gibbs and SRB distributions -- 6.1. Variational properties of Gibbs distributions -- 6.2. Applications to Ansov systems; SRB distribution -- 6.3. Periodic orbits, invariant probability distributions and entropy -- 6.4. Equivalent potentials; Gibbs distributions with transitive vacuum -- 7. Analyticity, singularity and phase transitions -- 7.1. Polymers -- 7.2. Cluster expansions -- 7.3. Renormalization by decimation in one-dimensional systems -- 7.4. Absence of phase transitions: More criteria -- 7.5. Phase transitions -- 8. Special ergodic theory problems in nonchaotic dynamics -- 8.1. Theory of quasi-periodic Hamiltonian motions -- 8.2 Graphs and diagrams for the Lindstedt series -- 8.3. Cancellations -- 8.4. Convergence and the KAM theorem -- 9. Some special topics in KAM theory -- 9.1. Resummations and renormalized series for invariant tori -- 9.2. Bounds on renormalized series; Convergence -- 9.3. Scaling laws for the standard map -- 9.4. Limit function for the standard map near resonances -- 10. Special problems in chaotic dynamics -- 10.1. Perturbing Arnold's cat map -- 10.2. Extending systems; Lattices of Arnold's cat maps -- 10.3. Chaos in time: An SRB distribution -- 10.4. Chaos in space-time and SRB distributions -- 10.5. Isomorphisms -- Appendix A: Nonequilibrium thermodynamics? Twenty-seven comments
Control code
52902662
Dimensions
25 cm
Extent
x, 435 pages
Isbn
9783540408796
Isbn Type
(acid-free paper)
Lccn
2003061491
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
Label
Aspects of ergodic, qualitative, and statistical theory of motion, G. Gallavotti, F. Bonetto, G. Gentile
Publication
Bibliography note
Includes bibliographical references (pages [411]-421) and indexes
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1. General qualitative properties -- 1.1. Historical note -- 1.2. Examples and some definitions -- 1.3. Harmonic oscillators and integrable systems as dynamical systems -- 1.4. Frequencies of visit -- 2. Ergodicity and ergodic points -- 2.1. Quasi-periodic motions and integrability -- 2.2. Ergodic properties of quasi-periodic motions; Ergodic sequences and measures -- 2.3. Ergodic points -- 2.4. Ergodic decomposition -- 3. Entropy and complexity -- 3.1. Complexity of motions and entropy -- 3.2. The Shannon-McMillan theorem -- 3.3. Elementary properties of the average entropy -- 3.4. Further properties of the average entropy; Generator theorem -- 4. Markovian pavements -- 4.1. Compatibility of histories; Markovian pavements -- 4.2. Markovian pavements for hyperbolic systems -- 4.3. Coding of the volume measure of smooth hyperbolic systems -- 5. Gibbs distributions -- 5.1. Gibbs distributions -- 5.2. Properties of Gibbs distributions -- 5.3. Gibbs distributions on Z+ -- 5.4. An application: Expansive maps of [0,1] -- 6. General properties of Gibbs and SRB distributions -- 6.1. Variational properties of Gibbs distributions -- 6.2. Applications to Ansov systems; SRB distribution -- 6.3. Periodic orbits, invariant probability distributions and entropy -- 6.4. Equivalent potentials; Gibbs distributions with transitive vacuum -- 7. Analyticity, singularity and phase transitions -- 7.1. Polymers -- 7.2. Cluster expansions -- 7.3. Renormalization by decimation in one-dimensional systems -- 7.4. Absence of phase transitions: More criteria -- 7.5. Phase transitions -- 8. Special ergodic theory problems in nonchaotic dynamics -- 8.1. Theory of quasi-periodic Hamiltonian motions -- 8.2 Graphs and diagrams for the Lindstedt series -- 8.3. Cancellations -- 8.4. Convergence and the KAM theorem -- 9. Some special topics in KAM theory -- 9.1. Resummations and renormalized series for invariant tori -- 9.2. Bounds on renormalized series; Convergence -- 9.3. Scaling laws for the standard map -- 9.4. Limit function for the standard map near resonances -- 10. Special problems in chaotic dynamics -- 10.1. Perturbing Arnold's cat map -- 10.2. Extending systems; Lattices of Arnold's cat maps -- 10.3. Chaos in time: An SRB distribution -- 10.4. Chaos in space-time and SRB distributions -- 10.5. Isomorphisms -- Appendix A: Nonequilibrium thermodynamics? Twenty-seven comments
Control code
52902662
Dimensions
25 cm
Extent
x, 435 pages
Isbn
9783540408796
Isbn Type
(acid-free paper)
Lccn
2003061491
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations

Subject

Member of

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