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El. knyga: Thermodynamic Formalism: CIRM Jean-Morlet Chair, Fall 2019

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  • Formatas: EPUB+DRM
  • Serija: Lecture Notes in Mathematics 2290
  • Išleidimo metai: 01-Oct-2021
  • Leidėjas: Springer Nature Switzerland AG
  • Kalba: eng
  • ISBN-13: 9783030748630
Kitos knygos pagal šią temą:
Thermodynamic Formalism: CIRM Jean-Morlet Chair, Fall 2019Didesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Serija: Lecture Notes in Mathematics 2290
  • Išleidimo metai: 01-Oct-2021
  • Leidėjas: Springer Nature Switzerland AG
  • Kalba: eng
  • ISBN-13: 9783030748630
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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.
- Part I Specifications and Expansiveness. - 1. Beyond Bowens
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 BorelCantelli Property in Conventional and Nonconventional
Setups. - 8. Application of the Convergence of the Spatio-Temporal Processes
for Visits to Small Sets. - 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.
- 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
Orponens Theorem on Visible Parts of Fractal Sets.
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