- Yakov Pesin and Vaughn Climenhaga, "Lectures on fractal geometry and dynamical systems", American Mathematical Society, 2009.
- Shlomo Sternberg, "Dynamical Systems", Dover, 2010.
- Paul Addison "Fractals and Chaos: an illustrated course", Institute of Physics Publishing, 1997.
- Christian Beck, Friedrich Schoegl, "Thermodynamic of chaotic systems", Cambridge University Press, 1993.
- Kenneth Falconer, "Fractal geometry" (2nd), Wiley, 2003.

- pdf Period three implies chaos (by T.Y.Li and A.Yorke)
- pdf Approximation of continuous Newton's method: an extension of Cayley's problem (by J.Jacobssen, O.Lewis, B.Tennis)
- pdf Chaos, fractals and statistics (S.Chatterjee and M.R.Yilmaz)
- pdf Arithmetic Quantum Chaos (Jens Marklof)
- pdf Arithmetic Quantum Chaos (Peter Sarnak)
- pdf What is quantum chaos? (Zeev Rudnick)
- pdf Multifractal analysis of Lyapunov exponent for Continued fraction and Manneville-Pomeau transformations and applications to Diophantine approximation (M.Pollicott and H.Weiss)
- pdf Multifractal of the Apollonian tiling (Dominique Simpelaere)
- pdf The multifractal analysis of Birkhoff averages and large deviations (Yakov Pesin and Howard Weiss)
- pdf A generalized multifractal spectrum of the general Sierpinski carpets (by Yongxin Gui and Wenxia Li)
- pdf Spectral triples and the geometry of fractals (by Erik Christensen, Christina Ivan, Elmar Schrohe)
- pdf Dirac operators and spectral triples for some fractal sets built on curves (by Erik Christensen, Cristina Ivan and Michael Lapidus)
- pdf Complex dimension of self-similar fractal strings and Diophantine approximations (by Michel Lapidus and Machiel van Frankenhuysen)
- pdf Fifty years of entropy in dynamics (by A.Katok)

- Tuesday April 1: Lorentz attractor: fixed points, linearization, Lyapunov function, pitchfork bifurcation, Hopf bifurcation, strange attractor; sensitive dependence on the initial conditions, Lyapunov exponent; definition of chaos
- Thursday April 3: Discrete dynamical systems, iterates, domains, cobweb diagrams, construction of the Cantor sets via domains of iterates of a piecewise linear map, coding space for the Cantor set
- Tuesday April 8: Topological spaces and metric spaces, cylinder sets and topology on the Cantor set, non-uniform Cantor sets
- Thursday April 10: Hausdorff measures and Hausdorff dimension, jumping infinity/zero, scaling behavior, estimate of the Hausdorff dimension of the Cantor set; scaling transformations and Lipschitz functions
- Tuesday April 15: guest lecture by Jan-Jitse Venselaar: Dirac operators and spectral triples on the circle and on tori
- Thursday April 17: guest lecture by Jan-Jitse Venselaar: a Dirac operator on the Cantor set, spectral triple, zeta function and the Hausdorff dimension
- Tuesday April 22: Fixed point theorem for contractions on complete metric spaces; the Hausdorff distance on nonempty compact subsets of a complete metric space; completeness of the Hausdorff distance; contraction maps in the Hausdorff distance and self-similar sets; the Cantor set and the Sierpinski gasket as self-similar sets
- Thursday April 24: topological dimension and relation to the Hausdorff dimension, Lipschitz and bi-Lipschitz functions and the Hausdorff dimension, topological consequences of small Hausdorff dimension (total disconnectedness)
- Tuesday April 29: box counting dimension and relation to the Hausdorff dimension, properties of box counting, examples with zero Hausdorff dimension and arbitrary lower and upper box counting dimensions between zero and one
- Thursday May 1: Measure theory: outer measures, sigma-algebras, measures from outer measures, Caratheodory construction, Dirac delta measure, counting measure, Lebesgue and Hausdorff measures, non-measurable sets: Banach-Tarsky paradox
- Tuesday May 6: Bernoulli probability measures on shift spaces, Markov measures on shift spaces, support of a measure, admissible words, admissibility matrix and subshifts of finite type
- Thursday May 8: Uniform mass distribution principle, lower bounds on the Hausdorff dimension from measures, local dimension, case of Cantor sets, relation to Shannon entropy, almost everywhere convergence of digit frequencies; ergodic measures, ergodicity of Bernoulli measures
- Tuesday May 13: Bowen balls, local entropy, invariance of entropy under topological conjugacy, topological entropy, entropy of Markov measures, Parry measures of maximal entropy and Perron-Frobenius theory of the admissibility matrix
- Thursday May 15: no class today: Ditch Day!
- Tuesday May 20:
- Thursday May 22:
- Tuesday May 27: Student presentations
- Thursday May 29: Student presentations
- Tuesay June 3: Student presentations
- Thursday June 5: Student presentations

- May 27, Sadaf Amouzegar: Approximations of continuous Newton's method
- May 27, Hugo Lavenant: Fifty years of entropy in dynamics
- May 29, Evan Patterson: The multifractal analysis of Birkhoff averages and large deviations
- May 29, Zachary Rivchin
- June 3, Melissa Zhang: Complex dimension of self-similar fractal strings and Diophantine approximations
- June 3, Taylor Sturmwasser: Period Three implies Chaos
- June 5, Anusha Sinha: What is Quantum Chaos?
- June 5, Daniel Guth: Spectral triples and the geometry of fractals

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