Winter 2023 teaching (Check the  DePaul D2L site for more info): 

        MAT 385/485 Numerical Analysis I   

Research Interests: Dynamical Systems, Smooth Ergodic Theory, Population Dynamics

The research work during 2007-2011 was partially supported by the NSF grant 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)

• A strongly aperiodic shift of finite type on the discrete Heisenberg group using Robinson tilings (with A. Şahin and M. Schraudner), Illinois Journ. of Math., 65 (2021), 655-686. arXiv:2009.077510

• Flexibility of entropy of boundary maps for surfaces of constant negative curvatures (with A. Abrams and S. Katok), Ergodic Theory and Dyn. Systems, 42 (2022), 389-401. arXiv:1909.07032

• Rigidity of topological entropy of boundary maps associated to Fuchsian groups (with A. Abrams and S. Katok), to appear in "A Vision For Dynamics: The Legacy of Anatole Katok", ed. Boris Hasselblatt et al., Cambridge University Press, arXiv:2101.10271

• Rigidity and flexibility of entropies of boundary maps associated to Fuchsian groups (with A. Abrams, S. Katok), Mathematics Research Reports, 3 (2022), 1-19. arXiv:2106.13779

• On the topological entropy of (a,b)-continued fraction transformations (with A. Abrams and S. Katok), preprint, arXiv:2210.07389

Some conferences I co-organized:

• Geometry, Topology and Number Theory  in honor of Svetlana Katok (May 5-6, '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 5-6, '07), Chicago
  

• AMS 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

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