Sonja Štimac - Dynamics of Henon and Lozi maps

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.