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Ergodic Theory and Fractal Geometry
About this Title
Hillel Furstenberg, The Hebrew University of Jerusalem, Jerusalem, Israel
Publication: CBMS Regional Conference Series in Mathematics
Publication Year:
2014; Volume 120
ISBNs: 978-1-4704-1034-6 (print); 978-1-4704-1854-0 (online)
DOI: https://doi.org/10.1090/cbms/120
MathSciNet review: MR3235463
MSC: Primary 37A20; Secondary 28A80, 37A30
Table of Contents
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Front/Back Matter
Chapters
- 1. Introduction to fractals
- 2. Dimension
- 3. Trees and fractals
- 4. Invariant sets
- 5. Probability trees
- 6. Galleries
- 7. Probability trees revisited
- 8. Elements of ergodic theory
- 9. Galleries of trees
- 10. General remarks on Markov systems
- 11. Markov operator $\mathcal {T}$ and measure preserving transformation $T$
- 12. Probability trees and galleries
- 13. Ergodic theorem and the proof of the main theorem
- 14. An application: The $k$-lane property
- 15. Dimension and energy
- 16. Dimension conservation
- 17. Ergodic theorem for sequences of functions
- 18. Dimension conservation for homogeneous fractals: The main steps in the proof
- 19. Verifying the conditions of the ergodic theorem for sequences of functions