An extension of quantitative nondivergence and applications to Diophantine exponents

DOI10.1090/S0002-9947-08-04592-3zbMath1230.37009arXivmath/0508517OpenAlexW1970724678MaRDI QIDQ3542012

Dmitry Kleinbock

Publication date: 27 November 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0508517

zbMATH Keywords

metric Diophantine approximations on manifoldspolynomial-like flows

Mathematics Subject Classification ID

Related Items (26)

Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. II: Analytic case. ⋮ Diophantine Inheritance for $p$-adic measures ⋮ Khintchine's theorem for affine hyperplanes in positive charateristic ⋮ An `almost all versus no' dichotomy in homogeneous dynamics and Diophantine approximation ⋮ Metric Diophantine approximation over a local field of positive characteristic ⋮ Quantitative disjointness of nilflows from horospherical flows ⋮ Positive measure of effective quasi-periodic motion near a Diophantine torus ⋮ Diophantine approximation on quadrics ⋮ Extremal affine subspaces and Khintchine-Jarník type theorems ⋮ The inhomogeneous Sprindžhuk conjecture over a local field of positive characteristic ⋮ On \(\epsilon\)-escaping trajectories in homogeneous spaces ⋮ On badly approximable subspaces ⋮ Diophantine approximation on matrices and Lie groups ⋮ On Diophantine transference principles ⋮ Diophantine exponents and the Khintchine Groshev theorem ⋮ METRIC DIOPHANTINE APPROXIMATION FOR SYSTEMS OF LINEAR FORMS VIA DYNAMICS ⋮ A KHINTCHINE–GROSHEV THEOREM FOR AFFINE HYPERPLANES ⋮ Multiplicative p-adic metric Diophantine approximation on manifolds and dichotomy of exponents ⋮ Diophantine exponents of affine subspaces: the simultaneous approximation case ⋮ Quantitative Diophantine approximation on affine subspaces ⋮ Badly approximable points on manifolds and unipotent orbits in homogeneous spaces ⋮ Winning property of badly approximable points on curves ⋮ Zimmer's conjecture for actions of \(\mathrm{SL}(m,\mathbb{Z})\) ⋮ Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents ⋮ On metric Diophantine approximation in matrices and Lie groups ⋮ Multiplicative Diophantine exponents of hyperplanes and their nondegenerate submanifolds

Cites Work

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