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Hausdorff dimension of divergent trajectories on homogeneous spaces
Published online by Cambridge University Press: 19 December 2019
Abstract
For a one-parameter subgroup action on a finite-volume homogeneous space, we consider the set of points admitting divergent-on-average trajectories. We show that the Hausdorff dimension of this set is strictly less than the manifold dimension of the homogeneous space. As a corollary we know that the Hausdorff dimension of the set of points admitting divergent trajectories is not full, which proves a conjecture of Cheung [Hausdorff dimension of the set of singular pairs, Ann. of Math. (2) 173 (2011), 127–167].
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- © The Authors 2019
Footnotes
Current address: Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstrasse 3-5, D-37073 Gottingen, Germany
L. G. is supported by EPSRC Programme Grant EP/J018260/1 and R. S. is supported by NSFC 11871158.
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