Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation

• Autores: Dmitry Kleinbock, Georges Tomanov
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 82, Nº 3, 2007, págs. 519-582
• Idioma: inglés
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• Resumen

  • The main goal of this work is to establish quantitative nondivergence estimates for flows on homogeneous spaces of products of real and p-adic Lie groups. These results have applications both to ergodic theory and to Diophantine approximation. Namely, earlier results of Dani (finiteness of locally finite ergodic unipotent-invariant measures on real homogeneous spaces) and Kleinbock¿Margulis (strong extremality of nondegenerate submanifolds of Rn) are generalized to the S-arithmetic setting.