Author:
AN JINPENG,GUAN LIFAN,KLEINBOCK DMITRY
Abstract
Abstract
Let G be a Lie group, let
$\Gamma \subset G$
be a discrete subgroup, let
$X=G/\Gamma $
and let f be an affine map from X to itself. We give conditions on a submanifold Z of X that guarantee that the set of points
$x\in X$
with f-trajectories avoiding Z is hyperplane absolute winning (a property which implies full Hausdorff dimension and is stable under countable intersections). A similar result is proved for one-parameter actions on X. This has applications in constructing exceptional geodesics on locally symmetric spaces and in non-density of the set of values of certain functions at integer points.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
3 articles.
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