Ilie D. Ugarcovici
Office: 520 Schmitt Academic Center
FALL 2019 teaching (Check the DePaul D2L site for more info):
MAT 384/484 Math Modeling and MAT 130 Precalculus
Research Interests: Dynamical Systems, Smooth Ergodic Theory, Population Dynamics
The research work during 2007-2011 was partially supported by the NSF
DMS-0703421. Research work between 2013-2019 supported by a Simons Foundation Collaboration Grant.
Publications and preprints:
Chaotic dynamics of a nonlinear density dependent population model (joint with H. Weiss), Nonlinearity 17 (2004), 1689-1711.
Geometrically Markov geodesics on the modular surface (joint with S. Katok) , Moscow Mathematical Journal 5 (2005), 135-151.
Arithmetic coding of geodesics on the modular surface via continued fractions (joint with S. Katok), CWI Tracts 135 (2005), Amsterdam, 59-77.
On hyperbolic measures and periodic orbits, Discrete and Continuous Dynamical Systems 16 (2006), 505-512.
Symbolic dynamics for the modular surface and beyond (joint with S. Katok), Bull. Amer. Math. Soc. 44 (2007), 87-132.
Chaotic attractors and physical measures for some density-dependent population models (with H. Weiss), Nonlinearity 20 (2007), 2897-2906.
Theory of (a,b)-continued fraction transformations and applications (with S. Katok), Electron. Res. Ann. Math. Sci. 17 (2010), 20-33.
Structure of attractors for (a,b)-continued fraction transformations (with S. Katok), Journal of Modern Dynamics 4 (2010), 637-691.
Applications of KAM Theory to Population Dynamics (with M. Gidea, J. Meiss and H. Weiss), Journal of Biological Dynamics 5 (2011), 44-53.
Applications of (a,b)-continued
fraction transformations (with S. Katok),
Ergodic Theory and Dyn. Systems 32 (2012), 755-777.
The structure and spectrum of Heisenberg odometers (with S. Lightwood and A. Şahin), Proc. Amer. Math. Soc. 142 (2014), 2429-2443.
Structure of attractors for boundary maps associated to Fuchsian groups (with S. Katok), Geometriae Dedicata, 191 (2017), 171-198. (See also Errata, Geom. Dedicata, 198 (2019), 189-191)
Some conferences I co-organized:
Geometry, Topology and
Number Theory in honor of Svetlana Katok (May 5-6, '07), Penn State
of Measurable and Smooth Dynamical Systems to Number Theory (Oct 4,
Special Session: Ergodic
Theory and Symbolic Dynamical Systems (Oct 5-6, '07), Chicago
Special Session: Smooth
Dynamical Systems (Oct 5-6, '07), Chicago
AIMS Special Session: Applied Hyperbolic and Elliptic Dynamics (May 24-29, 2010), Dresden
AMS Special Session: Ergodic and Symbolic Actions on Amenable Groups (Oct 3-4, '15), Chicago