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    An, Jinpeng Guan, Lifan and Kleinbock, Dmitry 2015. Bounded Orbits of Diagonalizable Flows on SL3(ℝ)/SL3(ℤ). International Mathematics Research Notices, Vol. 2015, Issue. 24, p. 13623.


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  • Ergodic Theory and Dynamical Systems, Volume 8, Issue 4
  • December 1988, pp. 523-529

On orbits of endomorphisms of tori and the Schmidt game

  • S. G. Dani (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385700004673
  • Published online: 01 September 2008
Abstract
Abstract

We show that there exists a subset F of the n-dimensional torus n such that F has Hausdorff dimension n and for any xF and any semisimple automorphism σ of n the closure of the σ-orbit of x contains no periodic points.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]S. G. Dani . Bounded orbits of flows on homogeneous spaces. Comment. Math. Helv. 61 (1986), 636660.

[3]R. Mane . Orbits of paths under hyperbolic toral automorphisms. Proc. Amer. Math. Soc. 73 (1979), 121125.

[4]W. M. Schmidt . On badly approximable numbers and certain games. Trans. Amer. Math. Soc. 123 (1966), 178199.

[5]W. M. Schmidt . Diophantine Approximation, Springer-Verlag: Berlin-Heidelberg-New York, 1980.

[6]P. Walters . An Introduction to Ergodic Theory, Springer-Verlag: Berlin-Heidelberg-New York, 1982.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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