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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.


Oleg Makarenkov (University of Texas at Dallas) - main organizer
Vladimir Dragovic (University of Texas at Dallas)
Dmitriy Rachinskiy (University of Texas at Dallas)


Vladimir Dragovic
Geometry and Dynamics of Elliptical Billiards

Dmitry Rachinskiy
Modeling and Analysis of Hysteresis Phenomena

Oleg Makarenkov
Stability and Bifurcations of Switched Systems
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

Program & Practical information:
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)
All lectures are in room GR 3.302 of the Green Hall building. Coffee breaks and poster sessions will take place right outside this room.

Breakfasts and lunches are available in Dining Hall West, see campus map. You will have to show your nametag to get your meal free of charge unless you informed me you decline having breakfast or dinner. Dining Hall doesn't close at 14:00 (you will be allowed to finish your lunch), but won't accept new orders after 14:00.

Important dates:

Registration July 20, 2015
On-campus guest house logging and dinning reservation July 1, 2015


Send a message to Oleg Makarenkov at to register for the school. Participation in the school is free. Please mention whether or not you are interested to present a poster during the school.

Financial support:

A limited number of logging and dinning grants is available for undegraduate and graduate students. To apply for financial support, please email your request to Oleg Makarenkov at, attach supporting documents (e.g. Bachelor transcripts and CV) and mention how participation in the school will burst your career.

Venue, Travel and Accommodation:

The school will take place in room GR 3.302 of Green Hall building of the University of Texas at Dallas (Richardson, TX 75080, USA). Please click Taxi from DFW airport to UT Dallas costs around $70 and takes roughly 45 mins of travel time.

On-campus logging and dinning will be arranged through UTD Residential Camp & Conference Services, please click for details.