Ergodic theory and fractal geometry

By: Furstenberg, HillelMaterial type: TextTextLanguage: English Series: Regional conference series in mathematics ; 120Publication details: Providence, Rhode Island, Conference Board of the Mathematical Sciences (CBMS) by the American Mathematical Society (AMS) 2017Edition: Indian EditionDescription: ix, 69 pISBN: 9781470437268 (PB)Subject(s): functions, and related topics Functional equations in the complex | Operator theory General theory of linear operators Ergodic theory | Mathematics
Contents:
Introduction to fractals Dimension Trees and fractals Invariant sets Probability trees Galleries Probability trees revisited Elements of ergodic theory Galleries of trees General remarks on Markov systems Markov operator T and measure preserving transformation T Probability trees and galleries Ergodic theorem and the proof of the main theorem An application : the k-lane property Dimension and energy Dimension conservation Ergodic theorem for sequences of functions Dimension conservation for homogeneous fractals : the main steps in the proof Verifying the conditions of the ergodic theorem for sequences of functions
Summary: Notes based on a series of lectures delivered at Kent State University in 2011
Item type: BOOKS
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Introduction to fractals
Dimension
Trees and fractals
Invariant sets
Probability trees
Galleries
Probability trees revisited
Elements of ergodic theory
Galleries of trees
General remarks on Markov systems
Markov operator T and measure preserving transformation T
Probability trees and galleries
Ergodic theorem and the proof of the main theorem
An application : the k-lane property
Dimension and energy
Dimension conservation
Ergodic theorem for sequences of functions
Dimension conservation for homogeneous fractals : the main steps in the proof
Verifying the conditions of the ergodic theorem for sequences of functions

Notes based on a series of lectures delivered at Kent State University in 2011

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The Institute of Mathematical Sciences, Chennai, India

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