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Sonja Štimac - Dynamics of Henon and Lozi maps

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Sonja Štimac, picture taken from the website.

Sonja Štimac is an Associate Professor at Department of Mathematics, Faculty of Science, University of Zagreb. Her research interests are: low - dimensional dynamical systems, topological and symbolic dynamics and inverse limit spaces. Moreover, she is a NEWFELPRO fellow from outgoing scheme. She implemented her project called „Dynamics of Henon and Lozi maps (HeLoMa)“ at the Indiana University – Purdue University Indianapolis under the mentorship of professor Michal Misiurewicz and at the Faculty of Science at University of Zagreb.

This project studies the dynamics of two-parameter families of horseshoe-like maps of plane such as the Hénon maps H_{a,b}(x,y) = (1+y-ax^2, bx) and the Lozi maps L_{a,b}(x, y) = (1+y-a|x|, bx). The fact that the Hénon-like attractors model the behavior of homoclinic tangencies dif-feomorphisms, makes them a universal structure in the onset of chaos. Additionally, the project is focused on resolving following six problems: (1) Study of periodic orbits of the horseshoe-like maps; (2) What is the dependence of topological entropy on parameters for the horseshoe-like maps; (3) What is exactly the set of parameters for which the Lozi map has a strange attractor; (4) Two parameters vs. infinitely many `kneading invariants’ - how to resolve this ambiguity; (5) There is a well-known connection between quadratic and tent interval maps. Is there anything like that for the Hénon and Lozi maps; (6) What are the simplest one-dimensional spaces for which attractors of the horseshoe-like maps are inverse limits?

During her NEWFELPRO project she wrote following scientific papers:

Disemination of her NEWFELPRO research results includes:

After completion of her NEWFELPRO experience, she was promoted to a full professor position at her Croatian institution and now she plans to develop a strong group at her department  that will work in dynamical systems. Also, she recently applied for an Austrian-Croatian bilateral grant.