Non-dense orbits on homogeneous spaces and applications to geometry and number theory

DOI10.1017/etds.2021.4zbMath1500.37001arXiv2001.05174OpenAlexW3136312478WikidataQ114118838 ScholiaQ114118838MaRDI QIDQ5863419

Lifan Guan, Jinpeng An, Dmitry Kleinbock

Publication date: 11 March 2022

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.05174

zbMATH Keywords

transversalityflows on homogeneous spacesnondense orbitshyperplane absolute winning

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Homogeneous flows (37A17) Relations between ergodic theory and number theory (37A44) Relations between ergodic theory and harmonic analysis (37A46)

Related Items (3)

Abundance of Dirichlet-improvable pairs with respect to arbitrary norms ⋮ A dichotomy phenomenon for bad minus normed Dirichlet ⋮ Non-dense orbits of systems with the approximate product property

Cites Work

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• Modified Schmidt games and non-dense forward orbits of partially hyperbolic systems
• On Schmidt's game and the set of points with non-dense orbits under a class of expanding maps
• Bounded orbits of flows on homogeneous spaces
• Winning sets, quasiconformal maps and Diophantine approximation
• Geodesic flows on symmetric Riemann spaces
• Invariant measures and the set of exceptions to Littlewood's conjecture
• Bounded orbits of Anosov flows
• Bounded geodesics in manifolds of negative curvature
• Invariant subsets of rank 1 manifolds
• Nondense orbits for Anosov diffeomorphisms of the \(2\)-torus
• Logarithm laws for flows on homogeneous spaces
• Metrical theorems on systems of affine forms
• Bounded orbits of diagonalizable flows on finite volume quotients of products of \(\mathrm{SL}_2(\mathbb{R})\)
• Modified Schmidt games and a conjecture of Margulis
• Badly approximable systems of affine forms and incompressibility on fractals
• Values of binary quadratic forms at integer points and Schmidt games
• Schmidt games and non-dense forward orbits of certain partially hyperbolic systems
• Schmidt’s game, fractals, and orbits of toral endomorphisms
• The set of badly approximable vectors is strongly C¹ incompressible
• Bounded Orbits of Diagonalizable Flows on SL₃(ℝ)/SL₃(ℤ)
• Divergent trajectories of flows on homogeneous spaces and Diophantine approximation.
• On orbits of endomorphisms of tori and the Schmidt game
• Nondense orbits of flows on homogeneous spaces
• Geodesics avoiding open subsets in surfaces of negative curvature
• Bounded orbits of certain diagonalizable flows on $SL_{n}(R)/SL_{n}(Z)$
• Flow invariant subsets for geodesic flows of manifolds with non-positive curvature
• Schmidt’s game and nonuniformly expanding interval maps
• A note on badly approximable affine forms and winning sets
• The Hausdorff dimension of the set of points with nondense orbit under a hyperbolic dynamical system
• On Badly Approximable Numbers and Certain Games
• On the product of three homogeneous linear forms and indefinite ternary quadratic forms

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