Speaker: Michal Misiurewicz (IUPUI)

Title: Entropy locking

Abstract: Consider discontinuous piecewise linear interval maps with two pieces, where the map is increasing on one piece and decreasing on the other piece. Often the topological entropy depends only on the slopes, not on the size of the jump at the discontinuity point. We present a simple explanation of this phenomenon. This is joint work with David Cosper.

Speaker: Kostya Medynets (US Naval Academy)

Title: Ergodic actions and characters of discrete groups

Abstract: Click here for pdf.

Speaker: Ben Webb (Brigham Young University)

Title: Intrinsic stability of time-delayed networks and multidimensional dynamical systems

Abstract: In real networks the time it takes to send and process information inevitably leads to time delays in the network’s dynamics. These time-delays are important to the network’s dynamics as they are often the source of instability and poor performance. In fact, time delays can both destabilize stable systems and stabilize unstable systems, depending on the system and where these delays are placed. In this talk we introduce a stronger notion of stability that is preserved under changes to a network’s structure of delays. This we call intrinsic stability, which can be used to simplify the stability analysis for both dynamical networks as well as multidimensional systems. This work is joint with L. A. Bunimovich.

Speaker: Joel Moreira (Ohio State)

Title: Non-linear monochromatic patterns in N via topological dynamics

Abstract: Since Furstenberg’s seminal paper in 1977 providing an ergodic theoretic proof of Szemeredi’s theorem on arithmetic progressions, dynamical systems methods have been a very successful tool in obtaining combinatorial results. A central problem in Ramsey theory is to understand and classify which polynomial patterns can be found “monochromatically” in any arbitrary finite coloring of the natural numbers. In particular, the question of whether any finite coloring of the natural numbers yields a monochromatic pattern of the form {x+y,xy} has remained unanswered for several years. In this talk I will investigate dynamical approaches to this and related questions, employing techniques from topological dynamics.