Contents
Preface ix
Chapter 1. Introduction to Fractals 1
Chapter 2. Dimension 11
Chapter 3. Trees and Fractals 15
Chapter 4. Invariant Sets 21
Chapter 5. Probability Trees 23
Chapter 6. Galleries 27
Chapter 7. Probability Trees Revisited 31
Chapter 8. Elements of Ergodic Theory 33
Chapter 9. Galleries of Trees 35
Chapter 10. General Remarks on Markov Systems 37
Chapter 11. Markov Operator T and Measure Preserving Transformation T 39
Chapter 12. Probability Trees and Galleries 43
Chapter 13. Ergodic Theorem and the Proof of the Main Theorem 47
Chapter 14. An Application: The k-lane property 51
Chapter 15. Dimension and Energy 53
Chapter 16. Dimension Conservation 55
Chapter 17. Ergodic Theorem for Sequences of Functions 57
Chapter 18. Dimension Conservation for Homogeneous Fractals: The Main
Steps in the Proof 59
Chapter 19. Verifying the Conditions of the Ergodic Theorem for Sequences
of Functions 65
Bibliography 67
Index 69
vii
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