TY  - BOOK
AU  - Furstenberg,Hillel
ED  - NSF-CBMS Regional Conference in the Mathematical Science on Ergodic Methods in the Theory of Fractals
ED  - National Science Foundation (U.S.)
TI  - Ergodic theory and fractal geometry
T2  - CBMS Regional Conference series in mathematics
SN  - 9781470410346 (softcover : alk. paper)
U1  - 510 23
PY  - 2014///
CY  - Providence
PB  - American Mathematical Society
KW  - Ergodic theory
KW  - Congresses
KW  - Fractals
N1  - "Support from the National Science Foundation."; Includes bibliographical references (page 67) and index; 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
Bibliography 
Index
N2  - The present monograph focuses on applications of one branch of dynamics--ergodic theory--to the geometry of fractals. Much attention is given to the all-important notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics
ER  -