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Flows on Homogeneous Spaces and Diophantine Approximation

In: Proceedings of the International Congress of Mathematicians

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  • S. G. Dani

    (Tata Institute of Fundamental Research)

Abstract

Let G be a Lie group and Γ be a lattice in G; that is, Γ is a discrete subgroup such that G/Γ admits a finite Borel measure invariant under the action of G (on the left). On the homogeneous spaceG/Γ there is a natural class of dynamical systems defined by the actions of subgroups ofG. The study of these systems has proved to be of great significance from the point of view of dynamics, ergodic theory, geometry, etc. and has found many interesting applications in number theory. The systems have been explored from various angles; however, I would like to concentrate here on giving an exposition of certain recent developments on the theme of the following classical theorem on orbits of what are called the horocycle flows.

Suggested Citation

  • S. G. Dani, 1995. "Flows on Homogeneous Spaces and Diophantine Approximation," Springer Books, in: S. D. Chatterji (ed.), Proceedings of the International Congress of Mathematicians, pages 780-789, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9078-6_71
    DOI: 10.1007/978-3-0348-9078-6_71
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