DYNAMICS IDEAS IN GEOMETRY, TOPOLOGY AND NUMBER THEORY
Conference Honoring Svetlana Katok's Birthday

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. My Google Scholar citation page.

BOOKS

MAIN MATHEMATICAL PUBLICATIONS

Rigidity and flexibility of entropies of boundary maps associated to Fuchsian groups (with Adam Abrams and Ilie Ugarcovici), Mathematics Research Reports, Volume 3 (2022), pp. 1-19.

Rigidity of topological entropy of boundary maps associated to Fuchsian groups (with Adam Abrams and Ilie Ugarcovici), to appear in the book "A Vision for Dynamics - The Legacy of Anatole Katok" published by Cambridge University Press.

Flexibility of measure-theoretical entropy of boundary maps associated to Fuchsian groups (with Adam Abrams and Ilie Ugarcovici), Ergod. Th. & Dynam Sys. 42 (2022), 389 - 401; First Online April 14 2021.

Adler and Flatto revisited: cross-section for geodesic flow on compact surfaces of constant negative curvature (with Adam Abrams), Studia Mathematica, 246 (2) (2019), 167 - 202.

Structure of attractors for boundary maps associated to Fuchsian groups (with Ilie Ugarcovici), Geometriae Dedicata, 191 (2017), 1, 171 - 198; First Online 16 May 2017.

Correction to: Structure of attractors for boundary maps associated to Fuchsian groups (with Ilie Ugarcovici), Geometriae Dedicata, 198, (2019), 189 – 191; First Online 06 March 2018.

The Fried average entropy and slow entropy for actions of higher rank abelian groups (with Anatole Katok and Federico Rodriguez Hertz), Geometric and Functional Analysis, 24 (2014), 1204 - 1228.

Applications of (a,b)-continued fraction transformations  (with Ilie Ugarcovici), Ergod. Th. & Dynam. Sys., 32 (2012), 755 - 777.

Structure of attractors for (a,b)-continued fraction transformations  (with Ilie Ugarcovici), Journal of Modern Dynamics, 4 (2010), 637 - 691.

Theory of (a,b)-continued fraction transformations and applications  (with Ilie Ugarcovici), Electron. Res. Announc. Math. Sci. 17 (2010), 20 - 33.

Fuchsian groups and geodesic flows on surfaces of constant negative curvature, Clay Mathematics Proceedings, Vol. 10, 243 – 320, Amer. Math. Soc., Providence, RI, 2010.

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

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

Heegner points, cycles and Maass forms, (with Peter Sarnak), Israel J. Math.,  84, (1993), 1–2, 193–227.

Elliptic operators and solutions of cohomological equations for geodesic flows with hyperbolic behavior, International Journal of Mathematics  2, 6, (1991), 701–709.

Approximate solutions of cohomological equations associated with some Anosov flows,  Ergod. Th. & Dynam. Sys.10 (1990), 367-379

Finite spanning sets for cusp forms and a related geometric result,  J. für d. reine und angewandte Math. 395 (1989), 186-195.

Eichler-Shimura homology, intersection numbers and rational structures on spaces of modular forms,   Transactions Am. Math. Soc.300, 2 (1987), 737-757

Reduction theory for Fuchsian groups,   Math. Ann.273 (1986), 461-470.

Closed geodesics, periods and arithmetic of modular forms,  Invent. Math.80 (1985), 469-480

Modular forms associated to closed geodesics and arithmetic applications,  Bull. Am. Math. Soc.11 (1984), 177-179.

The estimation from above for the topological entropy of a diffeomorphism,  Global Theory of Dynamical Systems, Springer, Lecture Notes in Mathematics819 (1980), 258-264.

Bifurcation sets and integral manifolds in the rigid body problem, (in Russian),  Uspehi Mat. Nauk 2 (164) (1972), 126-133, (Appendix to the Russian translation of "Topology and Mechanics" by S. Smale)

Linear extensions of dynamic systems and the reducibility problem,  Mathematical Notes of the Academy of Sciences of the USSR (A translation of Math. Zametki)  8, 4 (1970), 722-728.
 

OTHER PUBLICATIONS AND LECTURE NOTES

Anatole Katok Center for Dynamical Systems and Geometry (with Yakov Pesin),  Notices of American Math. Society, 66, 5 (2019), 720-721.

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 Research Programs,  (J. A. Gallian, ed.), The American Mathematical Society,  Providence,  Rhode Island, 133-138, 2000

MASS Program at Penn State (with Anatole Katok),  in Proceedings of the Conference on Summer  Undergraduate Mathematics Research 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.