PUBLICATIONS OF SVETLANA KATOK

My research interests include automorphic forms, analysis on Riemannian manifolds and symmetric spaces, hyperbolic geometry and Fuchsian groups, and application of dynamical systems to analysis and number theory. My most recent work was devoted to study of coding of geodesics on the modular surface. For all publications listed in MathSciNet click here.

BOOKS

MATHEMATICAL PREPRINTS

RECENT MATHEMATICAL PUBLICATIONS

Symbolic dynamics for the modular surface and beyond  (with Ilie Ugarcovici), Bull. of the Amer. Math. Soc., 44, no. 1 (2007), 87-132; electronically published on October 2, 2006

Higher cohomology for abelian groups of toral automorphisms II: the partially hyperbolic case, and corrigendum (with Anatole Katok), Ergod. Th. & Dynam. Sys.25 (2005), 1909-1917

Arithmetic coding of geodesics on the modular surface via continued fractions  (with Ilie Ugarcovici), CWI tracts, 135 (2005), 59-77

Geometrically Markov geodesics on the modular surface,  (with Ilie Ugarcovici), Moscow Mathematical Journal, 1 (2005), 135-155

Livshitz Theorem for the unitary frame flow  with an Appendix: Spanning sets for cusp forms on complex hyperbolic spaces by T. Foth and S. Katok, Ergod. Th. & Dynam. Sys.24 (2004), 127-140

Rigidity of measurable structure for Zd actions by automorphisms of a torus,  (with Anatole Katok and Klaus Schmidt), Comment. Math. Helv.,  77, no. 4 (2002), 718-745

Arithmetic coding and entropy for the positive geodesic flow on the modular surface  (with Boris Gurevich),  Moscow Mathematical Journal, 1, no. 4 (2001), 569-582

Spanning sets for automorphic forms and dynamics of the frame flow on complex hyperbolic spaces  (with Tatyana Foth),  Ergod. Th. & Dynam. Sys.21 (2001), 1071-1099

Rigidity of measurable structure for algebraic actions of higher-rank abelian groups, Abstracts AMS, 950-58-459, (1999)

Coding of closed geodesics after Gauss and Morse, Geom. Dedicata,  63 (1996), 123-145

Higher cohomology for abelian groups of toral automorphisms, (with Anatole Katok),  Ergod. Th. & Dynam. Sys.15 (1995), 569-592    Corrigendum
 

OTHER PUBLICATIONS AND LECTURE NOTES

p-adic analysis in comparison with real, in MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics, 11-87, AMS, Providence, 2003

Continued fractions, hyperbolic geometry and quadratic forms, in MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics, 121-160, AMS, Providence, 2003

MASS Program at Penn State (with Anatole Katok and Sergei Tabachnikov), Mathematical Intelligencer, 24, no. 4 (2002), 50-56

The MASS Program at Penn State (with S. Tabachnikov and A. Katok), Focus, 21, No. 2 (2001), 6

REU Summer Program at Penn State (with Moisey Guysinsky),  in Proceedings of the Conference on Summer  Undergraduate Mathematics Reseach Programs,  (J. A. Gallian, ed.), The American Mahtematical Society,  Providence,  Rhode Island, 133-138, 2000

MASS Program at Penn State (with Anatole Katok),  in Proceedings of the Conference on Summer  Undergraduate Mathematics Reseach Programs,  (J.A. Gallian, ed.), The American Mahtematical Society,  Providence,  Rhode Island, 307-314, 2000

Teaching geometry in the MASS program at Penn State, Abstracts AMS, 939-98-540 , (1998)

To the new era of electronic communication with ERA-AMS, Abstracts AMS, 939-99-542 , (1998)

Arithmetic and geometry of the unimodular group, Lecture Notes of a MASS course  given at Penn State in Fall 1997, 60 pp.

What is Number? in Women in Mathematics: Scaling the Heights, (D. Nolan, ed.), The Mathematical Association of America, Washington D.C.,  67-75, 1997

Automorphic Forms, Lecture Notes of a graduate course given at Penn State in Spring 1995, 94 pp.