Ergodic Theory and Dynamical Systems Seminar

Title:  Benford’s Law:  Detecting fraud in business using ergodic theory Abstract:  Benford’s Law is the observation that in many collections of numbers like mathematical tables or real-life data,  the leading significant digits are not uniformly distributed, as might be expected, … Read more

Title: Guessing the present from observations at random times in the future Abstract: In order to try to understand average information obtained from measurements made at random times, we consider very simple Markov chains, and even a switch of two points, … Read more

Title: What is Ergodic Theory? Abstract:This will be an hour chalk talk where the basic ideas, theorems, and examples in ergodic theory are introduced with their physical roots and some current applications.

Title: A well-known but still fascinating example in ergodic theory: The Gauss Map   Abstract:  Defining Tx to be the fractional part of 1/x for x in the unit interval produces a map that is isomorphic to the shift map … Read more

Title: From billiards in the T-fractal to non-singular transformations Abstract: The motion of an ideal point-mass in a self-similar polygonal region in the plane, called the T-fractal, naturally leads to the study of an infinite interval exchange. The self-similarity of this … Read more

Title:  Odometers, Substitutions, and Bounded Topological Speedups Abstract: In dynamics, when we study a transformation of a space T:X->X, we often take the point of view that the action of T represents the passage of a unit of time, and thus by studying … Read more

Title:  Dynamical systems and Julia sets on the real projective plane Abstract:   This talk is based on joint work with Sue Goodman.   We discuss analytic maps of the sphere that project to well-defined maps on the nonorientable real surface RP2 … Read more

Title: Periodic Cycles of Social Activity Abstract:  In this talk I will begin by introducing a 2x2 dynamical system with a time-periodic source term, which can be seen as a toy model for the dynamics social outbursts.  It consists of an … Read more

Title:  Herman Rings and Siegel disks: the two most interesting Fatou components in complex dynamics Abstract: It is known that there are five different types of forward invariant components of the Fatou sets of rational maps. Two particularly interesting types of … Read more

Title: Beyond Pisot dynamics Abstract:  Pisot conjecture states that  substitutive  Pisot dynamics  implies  pure  discrete spectrum. We discuss in this lecture current extensions  with non-algebraic parameters, obtained  in collaboration with W. Steiner and J. Thuswaldner.  The Pisot assumption is formulated  in terms of Lyapunov … Read more