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:

• Jäger, Tobias, Alejandro Passeggi, and Sonja Štimac. "Rotation sets and almost periodic sequences." Mathematische Zeitschrift 284.1-2 (2016): 271-284.
• Misiurewicz, Michal, and Sonja Štimac. "Symbolic dynamics for Lozi maps." Nonlinearity 29.10 (2016): 3031.
• Bruin, Henk, and Sonja Stimac. "On isotopy of self-homeomorphisms of quadratic inverse limit spaces." arXiv preprint arXiv:1707.02238 (2017).

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.