Summer School on Nonsmooth Dynamical Systems will be held on August 4-6, 2015 at the University of Texas at Dallas. The three courses of the school will describe modern tools that help understanding the dynamics of Elliptical Billiards, Hysteresis Phenomena and Switched Systems. The elliptical billiards provide instructive examples of integrable systems; their dynamical properties follow from the geometry of pencils of conics and the arithmetic of related elliptic curves. The switched systems component will be centered around bifurcation theory, which proved to be a powerful tool in predicting limit cycles in anti-lock braking systems, passive walking robots, and other engineering models. Finally, the school will cover the infinite-dimensional operator framework required to model hysteresis phenomena that are common in plasticity, magnetism, friction, sorption, phase transitions, smart materials, biology and economics. Limited financial support is available for undergraduate and master students.
Courses: |
Vladimir Dragovic Geometry and Dynamics of Elliptical Billiards |
Dmitry Rachinskiy Modeling and Analysis of Hysteresis Phenomena |
Oleg Makarenkov Stability and Bifurcations of Switched Systems Slides Lecture notes Mathematica code Suggested reading: [1] M. Garcia, A. Chatterjee, A. Ruina, M. Coleman, The simplest walking model: Stability, complexity, and scaling, J. Biomech. Eng. 120 (1998), no. 2, 281-288. Journal link Preprint [2] M. Kamenskii, O. Makarenkov, P. Nistri, An alternative approach to study bifurcation from a limit cycle in periodically perturbed autonomous systems. J. Dynam. Differential Equations, 23 (2011), no. 3, 425-435. Journal link Preprint |
August 4 | August 5 | August 6 | |
7-8:30 | Breakfast (see below) | ||
8:30-9:45 | Vladimir Dragovic | Dmitry Rachinskiy | Oleg Makarenkov |
9:45-10:15 | Coffee Break & Poster Session | ||
10:15-11:30 | Oleg Makarenkov | Vladimir Dragovic | Dmitry Rachinskiy |
11:30-12:00 | Coffee Break & Poster Session | ||
12:00-13:15 | Dmitry Rachinskiy | Oleg Makarenkov | Vladimir Dragovic |
13:15-14:00 | Lunch (see below) |
Registration | July 20, 2015 |
On-campus guest house logging and dinning reservation | July 1, 2015 |