Thermodynamic Formalism
CIRM Jean-Morlet Chair, Fall 2019
Published on 2. October 2021
Book
Paperback/Softback
XIV, 536 pages
978-3-030-74862-3 (ISBN)
Description
This volume arose from a semester at CIRM-Luminy on "Thermodynamic Formalism: Applications to Probability, Geometry and Fractals" which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area.
Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry.
This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.
Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry.
This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.
More details
Series
Edition
1st ed. 2021
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
13 s/w Abbildungen, 8 farbige Abbildungen
XIV, 536 p. 21 illus., 8 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 30 mm
Weight
826 gr
ISBN-13
978-3-030-74862-3 (9783030748623)
DOI
10.1007/978-3-030-74863-0
Schweitzer Classification
Other editions
Additional editions
E-Book
10/2021
Springer
€69.54
Available for download
Content
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Part I Specifications and Expansiveness. -
1. Beyond Bowen's Specification Property. - 2. The Role of Continuity and Expansiveness on Leo and Periodic Specification Properties.
-
Part II Low Dimensional Dynamics and Thermodynamics
Formalism. -
3. Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions.
-
Part III Probability Theory Ergodicity and Thermodynamic
Formalism. -
4. Recurrent Sets for Ergodic Sums of an Integer Valued Function. - 5. Almost Sure Invariance Principle for Random Distance Expanding Maps with a Nonuniform Decay of Correlations. - 6. Limit Theorem for Reflected Random Walks. - 7. The Strong Borel-Cantelli Property in Conventional and Nonconventional Setups. - 8. Application of the Convergence of the Spatio-Temporal Processes for Visits to Small Sets.
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Part IV Geometry and Thermodynamics Formation. -
9. Rate of Mixing for Equilibrium States in Negative Curvature and Trees. - 10. Statistical Properties of the Rauzy-Veech-Zorich Map. - 11. Entropy Rigidity, Pressure Metric, and Immersed Surfaces in Hyperbolic 3-Manifolds. - 12. Higher Teichmüller Theory for Surface Groups and Shifts of Finite Type.
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Part V Fractal Geometry. -
13. Dimension Estimates for C1 Iterated Function Systems and C1 Repellers, a Survey. - 14. Intermediate Dimensions: A Survey. - 15. Fractal Geometry of Bedford-McMullen Carpets. - 16. Some Variants of Orponen's Theorem on Visible Parts of Fractal Sets.