Conference: Flexibility and Rigidity in Dynamical Systems

Suny At Stony Brook, Stony Brook NY

Investigators

Abstract

The workshop "Flexibility and Rigidity in Dynamical Systems” will be held from March 7 to March 11, 2022 at the Simons Center for Geometry and Physics at Stony Brook University. Dynamical systems model the time evolution of physical, biological or mathematical systems, such as planetary motion, fluid flows, or the progression of diseases. Several fundamental concepts and ideas, such as entropy, chaos and attractors, have been developed to describe such systems. Tools from symbolic dynamics have proved important in developing fast and safe codes in computer science. Hyperbolic dynamical systems naturally arise in electrical systems and their network problems. They also have applications within mathematics, especially to number theory, mathematical physics and geometry. This workshop will bring together experts in the dynamical systems areas of rigidity and flexibility, as well as a large group of graduate students and young researchers, to open new research avenues. The primary goal is to foster collaboration and build a community of researchers engaged in studying the interplay between flexibility and rigidity in dynamics. The workshop includes three mini-courses in addition to research talks and a problem session. The proximity of Stony Brook to many education and research institutions lends itself particularly well to dissemination of new research directions. The workshop will focus on fine properties of hyperbolic dynamical systems, i.e., systems whose orbits diverge exponentially fast - as it is typical in many situations. Mathematicians introduced invariants, in particular entropy and Lyapunov exponents, to describe their behavior. One can naturally ask for the range these invariants can take in a given class of dynamical systems (“flexibility”). Such ranges can be very restrictive, for example, when the systems exhibit extra symmetries. Sometimes this leads to a complete description of the systems (“rigidity”). While investigations on rigidity started half a century ago, work on flexibility started only recently. Highlights of recent research will form the core of the mini-courses of the workshop, especially new advances on rigidity of hyperbolic dynamical systems, entropy properties of negatively curved manifolds, and flexibility of group actions on the circle. The conference website is at: http://scgp.stonybrook.edu/archives/33724 This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.