2-dimensional badly approximable vectors and Schmidt's game

DOI10.1215/00127094-3165862zbMath1410.11095arXiv1204.3610OpenAlexW3123281856WikidataQ60731995 ScholiaQ60731995MaRDI QIDQ254762

Jinpeng An

Publication date: 16 March 2016

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.3610

zbMATH Keywords

badly approximable vectorSchmidt's game

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Simultaneous homogeneous approximation, linear forms (11J13) Metric theory (11J83) Diophantine approximation in probabilistic number theory (11K60)

Related Items (16)

On non-dense orbits of certain non-algebraic dynamical systems ⋮ Badly approximable points on planar curves and winning ⋮ Sets of inhomogeneous linear forms can be not isotropically winning ⋮ Badly approximable points on manifolds ⋮ A NOTE ON BADLY APPROXIMABLE LINEAR FORMS ON MANIFOLDS ⋮ A variational principle in the parametric geometry of numbers ⋮ A NOTE ON WEIGHTED BADLY APPROXIMABLE LINEAR FORMS ⋮ Badly approximable points in twisted Diophantine approximation and Hausdorff dimension ⋮ Bounded orbits of certain diagonalizable flows on $SL_{n}(R)/SL_{n}(Z)$ ⋮ The topological entropy of non-dense orbits and generalized Schmidt games ⋮ Badly approximable points on planar curves and a problem of Davenport ⋮ \(\mathbf{Bad(w)}\) is hyperplane absolute winning ⋮ Badly approximable points on manifolds and unipotent orbits in homogeneous spaces ⋮ Bounded orbits of diagonalizable flows on finite volume quotients of products of \(\mathrm{SL}_2(\mathbb{R})\) ⋮ Winning property of badly approximable points on curves ⋮ Modified Schmidt games and non-dense forward orbits of partially hyperbolic systems

Cites Work

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• On a question of N. Chevallier related to simultaneous Diophantine approximation
• On a problem in simultaneous Diophantine approximation: Schmidt's conjecture
• Winning sets, quasiconformal maps and Diophantine approximation
• Modified Schmidt games and Diophantine approximation with weights
• Invariant measures and the set of exceptions to Littlewood's conjecture
• Open problems in dynamics and related fields
• Dirichlet's theorem on Diophantine approximation and homogeneous flows
• Diophantine approximation
• Flows on homogeneous spaces and Diophantine properties of matrices.
• Modified Schmidt games and a conjecture of Margulis
• Badly approximable systems of linear forms
• On Simultaneously Badly Approximable Numbers
• The set of badly approximable vectors is strongly C¹ incompressible
• Divergent trajectories of flows on homogeneous spaces and Diophantine approximation.
• Bad(s,t) is hyperplane absolute winning
• Badziahin-Pollington-Velani's theorem and Schmidt's game
• On Badly Approximable Numbers and Certain Games

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