NEWFELPRO - 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:

Three seminars at Dynamic Seminar at Department of Mathematical Sciences, IUPUI: Horseshoe-like maps and symbolic dynamics I, II & III (September 2014)
One seminar at Geometry, Topology and Dynamics Seminar at Department of Mathematics, Statistics, and Computer Science, University of Illionis at Chicago: Horseshoe-like maps and symbolic dynamics (October 2014)
One seminar at Topology Seminar at Department of Mathematics, University of Zagreb; Horseshoe-like maps and symbolic dynamics (January 2015)
Joint Mathematics Meeting, San Antonio, Texas - Horseshoe-like maps and symbolic dynamics (January 2015)
49th Spring Topology and Dynamics Conference, Bowling Green, Ohio (May 2015)
Dubrovnik VIII – Geometric Topology, Geometric Group Theory & Dynamical Sytems, Dubrovnik, Croatia – Lazi maps and symbolic dynamics (June 2015)
Workshop on Dynamical Systems and Continuum Theory, Vienna, Austria (June/July 2015)
She gave talk at the 50th Spring Topology and Dynamics Conference at the Baylor University, Waco, TX on Symbolic dynamics for Lozi maps (March 2016)
She gave talk at 6th Croatian Mathematical Congress, Zagreb (June 2016)
She attended 19th Galway Topology Colloqium, Universitity of Leicester, UK (June 2016)
She gave talk at the 31st Summer Conference on Topology and its Applications, Universitity of Leicester, UK (August 2016)
She attended the 51th Spring Toplogy and Dynamics Conference hosted by New Jersey City University, Jersedy City, NJ, and gave a talk Lozi-like maps (March 2017)
She gave a seminar talk at Dynamic Seminar at Department of Mathematical Sciences, IUPUI. (March 2017)
She attended the workshop Dynamical Systems and Perturbations in St. Petersburg, Russia – organized by the Chebyshev Laboratory of St. Petersburg State University and the Euler International Mathematical Institute,

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.