GETDYN

Geometric, Ergodic and Topological Analysis of Low-dimensional Dynamical Systems

Grant no. 2285 supported by Croatian Science Foundation $HRZZ$ (May 2015 - April 2019)

Key highlights:

Davor Dragičević was awarded state prize for science in 2017.
A book was published by Goran Radunović and Darko Žubrinić, together with professor Michel L. Lapidus from University of California, Riverside
A book was published by Davor Dragičević together with professors Luís Barreira and Claudia Valls.
Several worshops were organized.

Abstract:

Our scientific work will focus on advancement and further development of recent exciting and important results of the team members, published in the leading international journals (in the last 5 years 18 Q1 and 9 Q2 articles). The recent results include: Solution of the Ingram’s hypothesis and better understanding of attractors of Lozi map, one of the most studied dynamical systems (S. Štimac); Developing of new definitions of fractal invariants, and characterizations of limit cycles in terms of fractal dimension (V. Županović); Understanding of dynamics of well-known systems including the driven Frenkel-Kontorova model and the Navier-Stokes equation by applying ergodic-theoretical and related tools (S. Slijepčević), and Introducing, establishing and developing new fractal zeta functions as an important tool in dynamical systems (D. Žubrinić).

In addition to scientific advancement, our general objectives include establishing new fruitful research collaborations at the international level, as well as continuing existing productive and active collaboration with over 15 leading international universities. We will also make sure our research is more visible and with more impact, and will look for physical and engineering applications and collaborations. Finally, we plan to continue our track record of 5 students completing their PhD’s in the last three years, often in collaboration with the leading international universities and experts (Dijon, California Riverside), and that postdocs continue impactful research at the international level.

A focus of our project is also developing further our recently established Centre for Nonlinear Dynamics (www.math.hr/cnd) as a regional centre of research in dynamical systems, one of the key areas of pure and applied mathematics.

Principal investigator:

Siniša Slijepčević, Professor, Zagreb

Team members:

Ana Anušić, PhD student, Zagreb

Davor Dragičević, Postdoc, Rijeka

Lana Horvat-Dmitrović, Assistant Professor, Zagreb

Pavao Mardešić, Professor, Dijon, France

Marina Ninčević, Lecturer, Zagreb

Braslav Rabar, Postdoc, Zagreb

Goran Radunović, Postdoc, Zagreb

Maja Resman, Assistant Professor, Zagreb

Sonja Štimac, Associate Professor, Zagreb

Domagoj Vlah, Assistant Professor, Zagreb

Darko Žubrinić, Professor, Zagreb

Vesna Županović, Professor, Zagreb

Publications and Conferences

Papers