Dmitry Kleinbock's Publications

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Dynamics and number theory

Uniform Diophantine approximation with restrictions via total density of collections of subspaces (with L. Hong and V. Neckrasov), Preprint (2026), arXiv:2603.25988.

Constructing bounded orbits of special types on homogeneous spaces (with M. Einsiedler and A. Rao), Preprint (2025), arXiv:2511.16095.

Simultaneously bounded and dense orbits for commuting Cartan actions (with C. Wu), Preprint (2025), arXiv:2509.05272.

Submanifold-genericity of R^d-actions and uniform multiplicative Diophantine approximation (with P. Bandi and R. Fregoli), Preprint (2025), arXiv:2504.02258.

On multiplicatively badly approximable vectors (with R. Fregoli), J. Number Theory 278 (2026), 570–621.

Singularity, weighted uniform approximation, intersections and rates (with N. Moshchevitin, J. Warren and B. Weiss), Compositio Math. 161 (2025), no. 11, 2990–3016.

Dimension drop for escape on average in homogeneous spaces (with S. Mirzadeh), Discrete Contin. Dyn. Syst. 45 (2025), no. 5, 1653–1671.

Dimension drop for diagonalizable flows on homogeneous spaces (with S. Mirzadeh), J. Mod. Dyn. 20 (2024), 441–478.

The work of G. A. Margulis (with A. Eskin and D. Fisher), in: The Abel Prize 2018–2022, 433–479, Springer, Cham, 2024.

Metrical properties of functions of consecutive digits in Lüroth series (with Y. Zhang), Integers 24 (2024), Paper No. A67, 9 pp.

Equidistribution in the space of 3-lattices and Dirichlet-improvable vectors on planar lines (with N. de Saxcé, N. Shah and P. Yang), Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 25 (2024), no. 1, 565–604. 

A dichotomy phenomenon for Bad minus normed Dirichlet (with A. Rao), Mathematika 69 (2023), no. 4, 1145–1164.

Dynamical Borel-Cantelli lemma for recurrence under Lipschitz twists (with J. Zheng), Nonlinearity 36 (2023), no. 2, 1434–1460. 

Inhomogeneous Diophantine approximation for generic homogeneous functions (with M. Skenderi), Int. J. Number Theory 19 (2023), no. 6, 1269–1293. 

Metrical properties for the weighted products of multiple partial quotients in continued fractions (with A. Bakhtawar, M. Hussain and B. Wang), Houston J. Math. 49 (2023), no. 1, 159–194. 

Measure theoretic laws for lim sup sets defined by rectangles (with B. Wang), Adv. Math. 428 (2023), Paper No. 109154, 32 pp.

On the dimension drop conjecture for diagonal flows on the space of lattices (with S. Mirzadeh), Adv. Math. 425 (2023), Paper No. 109058, 46 pp.

Zero-one laws for eventually always hitting points in mixing systems (with I. Konstantoulas and F. Richter), Math. Res. Lett. 30 (2023), no. 3, 765–805.

Weighted uniform Diophantine approximation of systems of linear forms (with A. Rao), Pure Appl. Math. Q. 18 (2022), no. 3, 1095–1112. 

A measure estimate in geometry of numbers and improvements to Dirichlet's theorem (with A. Strömbergsson and S. Yu), Proc. London Math. Soc. (3) 125 (2022), no. 4, 778–824.

Abundance of Dirichlet-improvable pairs with respect to arbitrary norms (with A. Rao), Moscow J. Comb. Number Th. 11 (2022), 97–114.

Nondense orbits on homogeneous spaces and applications to geometry and number theory (with J. An and L. Guan), Ergodic Theory Dynam. Systems 42 (2022), no. 4, 1327–1372.

A zero-one law for uniform Diophantine approximation in Euclidean norm (with A. Rao), Internat. Math. Res. Not. 2022, no. 8, 5617–5657.

Intrinsic Diophantine approximation on quadric hypersurfaces (with L. Fishman, K. Merrill and D. Simmons), J. Eur. Math. Society 24 (2022), no. 3, 1045–1101.

Quantitative non-divergence and Diophantine approximation on manifolds (with V. Beresnevich), in: Dynamics, geometry, number theory: an impact of Margulis on modern mathematics, University of Chicago Press, 2022.

Critical loci of convex domains in the plane (with A. Rao and S. Sathiamurthy), Indag. Math. (N.S.) 32 (2021), no. 3, 719–728.

Singular vectors on manifolds and fractals (with N. Moshchevitin and B. Weiss), Israel J. Math. 245 (2021), no. 2, 589–613.

Khintchine-type theorems for values of subhomogeneous functions at integer points (with M. Skenderi), Monatsh. Math. 194 (2021), no. 3, 523–554.

Dimension estimates for the set of points with non-dense orbit in homogeneous spaces (with S. Mirzadeh), Math. Z. 295 (2020), 1355–1383.

A dynamical Borel-Cantelli lemma via improvements to Dirichlet's theorem (with S. Yu), Moscow J. Comb. Number Theory 9 (2020), no. 2, 101–122.

Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials (with N. Moshchevitin), Acta Arith. 190 (2019), 87–100.

An inhomogeneous Dirichlet theorem via shrinking targets (with N. Wadleigh), Compositio Math. 155 (2019), no. 7, 1402–1423.

Rational approximation on quadrics: a simplex lemma and its consequences (with N. de Saxcé), Enseign. Math. 64 (2018), no. 3/4, 459–476.

Hausdorff measure of sets of Dirichlet non-improvable numbers (with M. Hussain, N. Wadleigh and B. Wang), Mathematika 64 (2018), no. 2, 502–518.

A zero-one law for improvements to Dirichlet's Theorem (with N. Wadleigh), Proc. Amer. Math. Soc. 146 (2018), no. 5, 1833–1844.

Intrinsic Diophantine approximation on manifolds: General theory (with L. Fishman, K. Merrill and D. Simmons), Trans. Amer. Math. Soc. 370 (2018), no. 1, 577–599.

An application of lattice points counting to shrinking target problems (with X. Zhao), Disc. Cont. Dyn. Systems 38 (2018), no. 1, 155–168.

Singular systems of linear forms and non-escape of mass in the space of lattices (with S. Kadyrov, E. Lindenstrauss and G.A. Margulis), J. Anal. Math. 133 (2017), 253–277.

Pointwise equidistribution with an error rate and with respect to unbounded functions (with R. Shi and B. Weiss), Math. Annalen 367 (2017), no. 1–2, 857–879.

S-adic version of Minkowski's geometry of numbers and Mahler's compactness criterion (with R. Shi and G. Tomanov), J. Number Th. 174, 150–163 (2017).

Badly approximable S-numbers and absolute Schmidt games (with T. Ly), J. Number Theory 164 (2016), 13–42.

Dimension estimates for sets of uniformly badly approximable systems of linear forms (with R. Broderick), Int. J. Number Theory 11, no. 7 (2015), 2037–2054.

Bounded orbits of diagonalizable flows on SL3(R)/SL3(Z) (with J. An and L. Guan), Internat. Math. Res. Notices 2015, no. 24, 13623–13652.

Rational Approximation on Spheres (with K. Merrill), Israel J. Math. 209 (2015), no. 1, 293–322.

On the complexity of a putative counterexample to the $p$-adic Littlewood conjecture (with D. Badziahin, Y. Bugeaud and M. Einsiedler), Compositio Math. 151 (2015), 1647–1662.

Non-planarity and metric Diophantine approximation for systems of linear forms (with V. Beresnevich and G. A. Margulis), J. Number Th. Bordeaux 27 (2015), no. 1, 1–31.

Modified Schmidt games and a conjecture of Margulis (with B. Weiss), J. Mod. Dyn. 7 (2013), no. 3, 429–460.

Ergodic theory on homogeneous spaces and metric number theory, in: Mathematics of complexity and dynamical systems Vols. 1–3, 302–312, Springer, New York, 2012.

The set of badly approximable vectors is strongly C1 incompressible (with R. Broderick, L. Fishman, A. Reich and B. Weiss), Math. Proc. Cambridge Philos. Soc. 153 (2012), no. 2, 319–339.

On effective equidistribution of expanding translates of certain orbits in the space of lattices (with G. A. Margulis), in: Number theory, analysis and geometry, 385–396, Springer, New York, 2012.

Schmidt's game, fractals, and orbits of toral endomorphisms (with R. Broderick and L. Fishman), Ergodic Theory Dynam. Systems 31 (2011), no. 4, 1095–1107.

An `almost all versus no' dichotomy in homogeneous dynamics and Diophantine approximation, Geom. Dedicata 149 (2010), 205–218.

Metric Diophantine approximation for systems of linear forms via dynamics (with G. Margulis and J. Wang), Int. J. Number Theory 6 (2010), no. 5, 1139–1168.

Quantitative nondivergence and its Diophantine applications, in: Homogeneous flows, moduli spaces and arithmetic, 131–153, Clay Math. Proc., 10, Amer. Math. Soc., Providence, RI, 2010.

Schmidt's game, fractals, and numbers normal to no base (with R. Broderick, Y. Bugeaud, L. Fishman and B. Weiss), Math. Res. Lett. 17 (2010), no. 2, 307–321.

Modified Schmidt games and Diophantine approximation with weights (with B. Weiss), Adv, Math. 223 (2010), no. 4, 1276–1298.

An extension of quantitative nondivergence and applications to Diophantine exponents, Trans. Amer. Math. Soc. 360 (2008), 6497–6523.

Diophantine exponents of measures and homogeneous dynamics, Pure Appl. Math. Q. 4 (2008), 81–97.

Dirichlet's theorem on diophantine approximation and homogeneous flows (with B. Weiss), J. Mod. Dyn. 4 (2008), 43–62.

Measure rigidity and p-adic Littlewood-type problems (with M. Einsiedler), Compositio Math. 143 (2007), 689–702.

Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation (with G. Tomanov), Comm. Math. Helv. 82 (2007), 519–581; a Max Planck Institute preprint version here.

Badly approximable vectors on fractals (with B. Weiss), Israel J. Math. 149 (2005), 137–170.

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.

Baker-Sprindzhuk conjectures for complex analytic manifolds, in: Algebraic groups and arithmetic, 539–553, Tata Inst. Fund. Res., Mumbai, 2004.

Bounded geodesics in moduli space (with B. Weiss), Internat. Math. Res. Notices 2004, no. 30, 1551–1560.

On fractal measures and Diophantine approximation (with E. Lindenstrauss and B. Weiss), Selecta Math. 10 (2004), 479–523.

Extremal subspaces and their submanifolds, Geom. Funct. Anal. 13 (2003), no. 2, 437–466.

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.

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.

Some applications of homogeneous dynamics to number theory, in: Smooth ergodic theory and its applications, 639–660, Proc. Sympos. Pure Math. 69, AMS, Providence, RI, 2001.

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; a University of Bielefeld preprint version here.

Dynamical Borel-Cantelli lemmas for Gibbs measures (with N. Chernov), Israel J. Math. 122 (2001), 1–27.

Badly approximable systems of affine forms, J. Number Theory 79 (1999), no. 1, 83–102.

Logarithm laws for flows on homogeneous spaces (with G. A. Margulis), Invent. Math. 138 (1999), no. 3, 451–494; erratum in 211 (2018), no. 2, 855–862.

Bounded orbit conjecture and diophantine approximation, in: Lie groups and ergodic theory (Mumbai, 1996), 119–130, Tata Inst. Fund. Res., Bombay, 1998.

Flows on homogeneous spaces and Diophantine approximation on manifolds (with G. A. Margulis), Ann. Math. 148 (1998), 339–360.

Flows on homogeneous spaces and Diophantine properties of matrices, Duke Math. J. 95 (1998), 107–124.

Nondense orbits of flows on homogeneous spaces, Ergodic Theory Dynam. Systems 18 (1998), 373–396.

Nondense orbits of nonquasiunipotent flows and applications to Diophantine approximation, Ph.D. Thesis, Yale University, 1996.

Bounded orbits of nonquasiunipotent flows on homogeneous spaces (with G. A. Margulis), Amer. Math. Soc. Transl. (2) 171 (1996), 141–172.

Fluid dynamics

Inverse problems for fluid flows with moving boundary (with Yu. Hohlov), in: Lipa's legacy (New York, 1995), 297–317, Contemp. Math. 211, Amer. Math. Soc., Providence, RI, 1997.

On nonlinear interface dynamics in Hele-Shaw flows (with V. M. Entov and P. Etingof), European J. Appl. Math. 6 (1995), 399–420.

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.

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.

Free boundary flows in a rotating Hele-Shaw cell (with V. M. Entov and P. Etingof), Preprint (1991). (Russian)