Nonlinear Dynamics: New Directions

By Author: Todd Young
By Todd Young

This conference, dedicated to Valentin Afraimovich on the occasion of his 65th birthday, was held at CIMAT in Guanajuato, in the hills of central Mexico. The talks were diverse and covered some of the numerous fields to which Prof. Afraimovich has made significant contributions:

* Networks of Coupled Nonlinear Systems

* Complex Dynamics in Hamiltonian and Dissipative Systems

* Ergodicity and Mixing

* Models of Biological and Social Processes

The three days of the meeting included about 35 talks, each 30 minutes long. Many of the speakers were collaborators or students of Valentin Afraimovich. The great variety and depth of the talks was a fitting tribute to the contributions of Professor Afraimovich, or, as many of the participants call him "Uncle Valya." It was noted by several participants that Uncle Valya's success could be partly attributed to his exceptional intellectual ability that allows him to have deep insights into a variety of problems and partly to his exceptional personal qualities that enable him to work graciously with variety of collaborators. According to MathSciNet, Valya currently has 55 recorded collaborators. A brief biography of Prof. Afraimovich is available on



Professor Valentin Afraimovich at the conference.

One can get a taste of the variety of the conference and of Valya's contributions from some of the titles of talks: "Direction Lyapunov exponents in Cellular automata", "Spatial chaos of traveling waves have a unique velocity", "Smooth interval maps have symbolic extensions", "Sequential dynamics of a small neural network of synaptically coupled Morris-Lecar neurons", "Concentration inequalities for dynamical systems", and "Brain modes dynamics." On Wednesday the speakers included: Gustavo Martínez-Mekler, Mikhail Rabinovich, Jose Seade, Sandro Vaienti, Leonid Bunimovich, Vered Rom-Kedar, Vladimir Nekorkin, Michael Zaks, Albert Luo, Todd Young, Howard Weiss, and Anthony Quas. The meeting continued on Thursday with talks by Pierre Collet, Dima Dolgopyat, Dima Turaev, Konstantin Khanin, Nokolai Chernov, Nicolai Haydn, Alejandro Maass, Nikolai Rulkov, Jean-Rene Chazottes, Bastien Fernandez, Lev Tsimring, and Maurice Courbage. On Thursday evening the participants celebrated Afriaimovich's birthday with an excellent banquet held in the courtyard of CIMATEL, the hostel run by CIMAT. Following the dinner, Leonid Bunimovich moderated a session of speeches, toasts and even poetry in honor of Valya. The last day of talks featured: Raul Rechtman, Andrei Shilnikov, Igor Belykh, Mikhail Malkin, Lev Lerman, Peter Makienko, Lev Glevsky, Yevgeniy Gordon, and Gregori Polotovsky. The conference concluded with a lively discussion about future directions in dynamical systems.



Uncle Valya at CIMAT with (left) Konstantin Khanin and (right) Michael Zaks.

Visiting CIMAT and Guanajuato was in itself a treat for me. The facilities and hospitality of CIMAT were excellent. CIMAT sits on a hill overlooking the beautiful city of Gaunajuato, which is designated a UNESCO World Heritage Site.

The Organizing Committee consisted of: Jean-René Chazottes, CNRS-École Polytechnique, Xavier Gomez-Mont, CIMAT, Renato Iturriaga, CIMAT, Alexander Pisarchik, CIO, Gelasio Salazar, UASLP, Edgardo Ugalde, UASLP (Chair and 95% organizer).


Afraimovich at CIMATEL.

Financial support for the meeting was provided by CIMAT, CONACYT, Secrataria Educacion Publica, Universidad Autonoma San Luis Potosi and Sociedad Matematica Mexicana.


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