Dimension properties of Deterministics and Stochastic fractal sets
Web page: http://www.math.toronto.edu/ilia/MAT1006.2017/.
Class Location & Time: Mon, 1:00 - 2:00 PM and Wed, 12:00 PM - 2:00 PM; BA6180
Extra classes: September 25, October 16, October 30: 12:00-1:00pm; BA6180
No classes October 23 and 25
Instructor: Ilia Binder (firstname.lastname@example.org), BA6118.
- C. Bishop and Y. Peres, Fractals in Probability and Analysis, Cambridge University Press, Dec 22, 2016
- M. Zinsmeister, Thermodynamic Formalism and Holomorphic Dynamical Systems, American Mathematical Society; (November 1999)
- Minkowski dimension.
- Hausdorff dimension and measure.
- Self-similar attractors.
- Furstenberg Lemma.
- Packing dimension.
- Frostman Lemma.
- Products and Slices.
- Potential Theory and Dimension.
- Random Cantor sets.
- Billingsley Lemma and its applications.
- Dimension of a measure and Eggleston's Theorem.
- Shift as a model dynamical system.
- Pressure and topological entropy.
- Perron-Ruelle-Frobenius Theorem.