An ‘almost all versus no’ dichotomy in homogeneous dynamics and Diophantine approximation View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2010-12

AUTHORS

Dmitry Kleinbock

ABSTRACT

Let Y0 be a not very well approximable m × n matrix, and let be a connected analytic submanifold in the space of m × n matrices containing Y0. Then almost all are not very well approximable. This and other similar statements are cast in terms of properties of certain orbits on homogeneous spaces and deduced from quantitative nondivergence estimates for‘quasi-polynomial’ flows on the space of lattices. More... »

PAGES

205-218

References to SciGraph publications

  • 1996-05. Limit distributions of expanding translates of certain orbits on homogeneous spaces in PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES. SECTION A
  • 1999-12. Logarithm laws for flows on homogeneous spaces in INVENTIONES MATHEMATICAE
  • 2005-12. Badly approximable vectors on fractals in ISRAEL JOURNAL OF MATHEMATICS
  • 2003-02. Extremal subspaces and their submanifolds in GEOMETRIC AND FUNCTIONAL ANALYSIS
  • 2005-04. On fractal measures and diophantine approximation in SELECTA MATHEMATICA
  • 2004-02. Divergent trajectories on noncompact parameter spaces in GEOMETRIC AND FUNCTIONAL ANALYSIS
  • 1972. Discrete Subgroups of Lie Groups in NONE
  • 1932-12. Über das Maß der Menge allerS-Zahlen in MATHEMATISCHE ANNALEN
  • 2007-09. Diophantine vectors in analytic submanifolds of Euclidean spaces in SCIENCE IN CHINA SERIES A MATHEMATICS
  • 2009-09. Equidistribution of expanding translates of curves and Dirichlet’s theorem on diophantine approximation in INVENTIONES MATHEMATICAE
  • Journal

    TITLE

    Geometriae Dedicata

    ISSUE

    1

    VOLUME

    149

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10711-010-9477-8

    DOI

    http://dx.doi.org/10.1007/s10711-010-9477-8

    DIMENSIONS

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