Publications of Dmitry Kleinbock

Homogeneous spaces and number theory

(PDF) Bounded trajectories in homogeneous spaces of semisimple Lie groups, Workshops on Dynamical Systems and Related Topics (1994), Pennsylvania State University, 1995.
(PDF) Bounded orbits of nonquasiunipotent flows on homogeneous spaces (with G. A. Margulis), Amer. Math. Soc. Transl. (2) 171 (1996), 141-172.
(PDF) Nondense orbits of nonquasiunipotent flows and applications to Diophantine approximation, Ph.D. Thesis, Yale University, 1996.
(PDF) Nondense orbits of flows on homogeneous spaces, Ergodic Theory Dynam. Systems 18 (1998), 373-396.
(PDF) Flows on homogeneous spaces and Diophantine properties of matrices, Duke Math. J. 95 (1998), 107-124.
(PDF) Flows on homogeneous spaces and Diophantine approximation on manifolds (with G. A. Margulis), Ann. Math. 148 (1998), 339-360.
(PDF) Bounded orbit conjecture and diophantine approximation, in: Proceedings of the International Colloquium on Lie Groups and Ergodic Theory, TIFR, Mumbai, 1998, pp. 119-130.
(PDF) Badly approximable systems of affine forms, J. of Number Theory 79 (1999), 83-102.
(Abstract, PDF) Logarithm laws for flows on homogeneous spaces (with G. A. Margulis), Inv. Math. 138 (1999), 451-494.
(PDF) Dynamical Borel-Cantelli lemmas for Gibbs measures (with N. Chernov), Israel J. Math. 122 (2001), 1-27.
(Abstract, PDF) Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions (with V. Bernik and G. A. Margulis), Internat. Math. Res. Notices 2001, no. 9, 453-486 (and here is an eariler version).
(PDF) Some applications of homogeneous dynamics to number theory, in: Smooth ergodic theory and its applications, Proc. Sympos. Pure Math. 69, AMS, Providence, RI, 2001, 639-660.
(PDF) Dynamics of subgroup actions on homogeneous spaces of Lie groups and applications to number theory (with A. Starkov and N. Shah), in: Handbook on Dynamical Systems, Volume 1A, Elsevier Science, North Holland, 2002.
(Abstract, PDF) Metric Diophantine approximation: the Khintchine-Groshev theorem for non-degenerate manifolds (with V. Beresnevich, V. Bernik and G.A. Margulis), Moscow Math. J. 2 (2002), no. 2, 203-225.
(Abstract, PDF) Extremal subspaces and their submanifolds, 26 pages, Geom. Funct. Anal 13 (2003), no. 2, 437-466.
(PDF) Baker-Sprindzhuk conjectures for complex analytic manifolds, 12 pages, in: Algebraic groups and Arithmetic, TIFR, India, 2004, 539-553.
(Abstract, PDF) On fractal measures and Diophantine approximation (with E. Lindenstrauss and B. Weiss), Selecta Math. 10 (2004), 479-523.
(Abstract, PDF) Bounded geodesics in moduli space (with B. Weiss), Internat. Math. Res. Notices 2004, no. 30, 1551-1560.
(PDF) Badly approximable vectors on fractals (with B. Weiss), Israel J. Math. 149 (2005), 137-170.
(PDF) Friendly measures, homogeneous flows and singular vectors (with B. Weiss), in: Algebraic and Topological Dynamics, Contemp. Math. 385 (2005), AMS, Providence, RI, 2005, 281--292.
(PDF) Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation (with G. Tomanov), Comm. Math. Helv. 82 (2007), 519-581.
(PDF) Measure rigidity and p-adic Littlewood-type problems (with M. Einsiedler), Compositio Math. 143 (2007), 689-702.
(PDF) Diophantine exponents of measures and homogeneous dynamics, Pure Appl. Math. Q. 4 (2008), 81-97.
(PDF) An extension of quantitative nondivergence and applications to Diophantine exponents, Trans. Amer. Math. Soc. 360 (2008), 6497-6523.
(PDF) Dirichlet's theorem on diophantine approximation and homogeneous flows (with B. Weiss), J. Mod. Dyn. 4 (2008), 43-62.
(PDF) On effective equidistribution of expanding translates of certain orbits in the space of lattices (with G. A. Margulis), Preprint, 10 pages, 2007.
(PDF) Ergodic Theory on Homogeneous Spaces and Metric Number Theory (a survey for Encyclopedia of Complexity and Systems Science, Springer Verlag), 19 pages, 2007.
(PDF) Metric Diophantine approximation for systems of linear forms via dynamics (with G. Margulis and J. Wang), 27 pages, to appear in Int. J. Number Theory.
(PDF) An `almost all versus no' dichotomy in homogeneous dynamics and Diophantine approximation, 14 pages, to appear in Geom. Dedicata.
(PDF) Quantitative nondivergence and its Diophantine applications, Lecture Notes for Clay Institute Summer School (Pisa 2007), 26 pages, 2009.
(PDF) Schmidt's game, fractals, and numbers normal to no base (with R. Broderick, Y. Bugeaud, L. Fishman and B. Weiss), Preprint, 15 pages, to appear in Math. Res. Letters.
(PDF) Schmidt's game, fractals, and orbits of toral endomorphisms (with R. Broderick and L. Fishman), 14 pages, 2009.
(PDF) Modified Schmidt games and Diophantine approximation with weights (with B. Weiss), Advances in Math. 223 (2010), 1276-1298
(PDF) Modified Schmidt games and a conjecture of Margulis (with B. Weiss), 33 pages, 2010.
(PDF) The set of badly approximable vectors is strongly C1 incompressible (with R. Broderick, L. Fishman, A. Reich and B. Weiss, 18 pages, 2011.

Fluid dynamics

Free boundary flows in a rotating Hele-Shaw cell (with V. M. Entov and P. Etingof), preprint (1991). (Russian)
Hele-Shaw flows with a free boundary produced by multipoles (with V. M. Entov and P. Etingof), Izv. Ross. Akad. Nauk, 5 (1993), 121-127 (Russian); English transl. in Fluid Dynamics 28 (1993), 686-691.
Hele-Shaw flows with a free boundary produced by multipoles (with V. M. Entov and P. Etingof), European J. Appl. Math. 4 (1993), 97-120.
On nonlinear interface dynamics in Hele-Shaw flows (with V. M. Entov and P. Etingof), European J. Appl. Math. 6 (1995), 399-420.
(PDF) Inverse problems for fluid flows with moving boundary (with Yu. Hohlov), Proceedings of the Bers Colloquium, Contemp. Math. 211 (1997), 297-318.