Nondense Orbits of Flows on Homogeneous Spaces
نویسنده
چکیده
Let F be a nonquasiunipotent one-parameter (cyclic) subgroup of a unimodular Lie group G, Γ a discrete subgroup of G. We prove that for certain classes of subsets Z of the homogeneous space G/Γ, the set of points in G/Γ with F -orbits staying away from Z has full Hausdorff dimension. From this we derive applications to geodesic flows on manifolds of constant negative curvature.
منابع مشابه
Nondense Orbits of Nonquasiunipotent Flows and Applications to Diophantine Approximation Nondense Orbits of Nonquasiunipotent Flows and Applications to Diophantine Approximation
Nondense orbits of nonquasiunipotent flows and applications to Diophantine approximation Dmitry Y. Kleinbock Yale University 1996 Let G be a Lie group and Γ a lattice in G. Consider a partially hyperbolic (nonquasiunipotent) flow on the homogeneous space G/Γ. We prove that for certain classes of subsets Z of G/Γ, the set of points with orbits staying away from Z, even though it may have measure...
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