
Ilie D. Ugarcovici Associate
Professor & 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 20072011 was partially supported by the NSF
grant
DMS0703421. Research work between 20132019 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), 16891711.
Geometrically Markov geodesics on the modular surface (joint with S. Katok) , Moscow Mathematical Journal 5 (2005), 135151.
Arithmetic coding of geodesics on the modular surface via continued fractions (joint with S. Katok), CWI Tracts 135 (2005), Amsterdam, 5977.
On hyperbolic measures and periodic orbits, Discrete and Continuous Dynamical Systems 16 (2006), 505512.
Symbolic dynamics for the modular surface and beyond (joint with S. Katok), Bull. Amer. Math. Soc. 44 (2007), 87132.
Chaotic attractors and physical measures for some densitydependent population models (with H. Weiss), Nonlinearity 20 (2007), 28972906.
Theory of (a,b)continued fraction transformations and applications (with S. Katok), Electron. Res. Ann. Math. Sci. 17 (2010), 2033.
Structure of attractors for (a,b)continued fraction transformations (with S. Katok), Journal of Modern Dynamics 4 (2010), 637691.
Applications of KAM Theory to Population Dynamics (with M. Gidea, J. Meiss and H. Weiss), Journal of Biological Dynamics 5 (2011), 4453.
Applications of (a,b)continued
fraction transformations (with S. Katok),
Ergodic Theory and Dyn. Systems 32 (2012), 755777.
The structure and spectrum of Heisenberg odometers (with S. Lightwood and A. Şahin), Proc. Amer. Math. Soc. 142 (2014), 24292443.
Structure of attractors for boundary maps associated to Fuchsian groups (with S. Katok), Geometriae Dedicata, 191 (2017), 171198. (See also Errata, Geom. Dedicata, 198 (2019), 189191)
Flexibility of entropy of boundary maps for surfaces of constant negative curvatures (with A. Abrams, S. Katok), preprint, arXiv:1909.07032
Some conferences I coorganized:
Geometry, Topology and
Number Theory in honor of Svetlana Katok (May 56, '07), Penn State
Workshop
on Applications
of Measurable and Smooth Dynamical Systems to Number Theory (Oct 4,
'07), Chicago
AMS
Special Session: Ergodic
Theory and Symbolic Dynamical Systems (Oct 56, '07), Chicago
AMS
Special Session: Smooth
Dynamical Systems (Oct 56, '07), Chicago
AIMS Special Session: Applied Hyperbolic and Elliptic Dynamics (May 2429, 2010), Dresden
AMS Special Session: Ergodic and Symbolic Actions on Amenable Groups (Oct 34, '15), Chicago
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