Mathematics Research Communities

Week 3, June 19 – 24, 2017, Dynamical Systems: Smooth, Symbolic, and Measurable


Jon Chaika (University of Utah)
Vaughn Climenhaga (University of Houston)
Boris Hasselblatt (Tufts University)
Bryna Kra (Northwestern University)
Daniel Thompson (The Ohio State University)

Smooth dynamics, symbolic dynamics, and measurable dynamics are different branches of a single subject and each branch has its own questions and techniques. Many fundamental advances in the field have been made by understanding the relations among these branches, leading to developments such as symbolic models for smooth systems, topological models for measurable systems, and thermodynamic formalism. This rich interplay among the smooth, symbolic, and measurable theory is the focus of this workshop.

The workshop will explore questions of contemporary interest, including characterization of the space of invariant measures, statistical properties of distinguished invariant measures, and symbolic models for smooth systems. Classical theory tells us that in the best-understood settings, one obtains different answers in the high-complexity (hyperbolic) case from those one does in the low-complexity (zero entropy) case. We will describe this general dichotomy and focus on specific problems where the classical phenomena may or may not continue to hold, including (1) non-uniformly hyperbolic systems, (2) geodesic flow on manifolds beyond the compact negative curvature case, (3) commuting maps, and (4) flat surfaces and interval exchange transformations.

Full information and how to apply can be found here.

Contact Information

For further information, please contact Associate Executive Director at

Top of Page