Badly approximable systems of affine forms, fractals, and Schmidt games

DOI10.1515/CRELLE.2011.078zbMath1244.11071arXiv0912.2445OpenAlexW2964168273MaRDI QIDQ3103805

Jimmy Tseng, Manfred Einsiedler

Publication date: 12 December 2011

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.2445

zbMATH Keywords

diophantine approximationmetric number theorySchmidt winning sets

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Metric theory (11J83)

Related Items (21)

Hausdorff measure of sets of Dirichlet non-improvable affine forms ⋮ Limit points badly approximable by horoballs ⋮ Metrical theorems on systems of affine forms ⋮ Badly approximable points on planar curves and winning ⋮ Simultaneous dense and nondense orbits for commuting maps ⋮ Sets of inhomogeneous linear forms can be not isotropically winning ⋮ FULLY INHOMOGENEOUS MULTIPLICATIVE DIOPHANTINE APPROXIMATION OF BADLY APPROXIMABLE NUMBERS ⋮ On Hausdorff dimension in inhomogeneous Diophantine approximation over global function fields ⋮ A NOTE ON BADLY APPROXIMABLE LINEAR FORMS ON MANIFOLDS ⋮ A solution to a problem of Cassels and Diophantine properties of cubic numbers ⋮ Some remarks on inhomogeneous Diophantine approximations ⋮ Badly approximable points on self-affine sponges and the lower Assouad dimension ⋮ Badly approximable systems of affine forms and incompressibility on fractals ⋮ A NOTE ON WEIGHTED BADLY APPROXIMABLE LINEAR FORMS ⋮ Badly approximable points in twisted Diophantine approximation and Hausdorff dimension ⋮ Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces ⋮ The topological entropy of non-dense orbits and generalized Schmidt games ⋮ Multiple mixing for a class of conservative surface flows ⋮ An inhomogeneous Dirichlet theorem via shrinking targets ⋮ Badly approximable affine forms and Schmidt games ⋮ Winning property of badly approximable points on curves

Cites Work

• Metric Diophantine approximation and `absolutely friendly' measures
• Schmidt's game on fractals
• Modified Schmidt games and Diophantine approximation with weights
• On circle rotations and the shrinking target properties
• Schmidt's game, badly approximable matrices and fractals
• Badly approximable affine forms and Schmidt games
• Badly approximable systems of affine forms
• Badly approximable systems of linear forms

This page was built for publication: Badly approximable systems of affine forms, fractals, and Schmidt games