Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-12-01T05:03:06.086Z Has data issue: false hasContentIssue false
  • English
  • Français

On orbits of endomorphisms of tori and the Schmidt game

Published online by Cambridge University Press:  19 September 2008

S. G. Dani
S. G. Dani
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 4 , December 1988 , pp. 523 - 529
Copyright
Copyright © Cambridge University Press 1988

References

REFERENCES

[1]Dani, S. G.. Bounded orbits of flows on homogeneous spaces. Comment. Math. Helv. 61 (1986), 636–660.CrossRefGoogle Scholar
[2]Dani, S. G.. On badly approximable numbers, Schmidt games and bounded orbits of flows. Preprint.Google Scholar
[3]Mane, R.. Orbits of paths under hyperbolic toral automorphisms. Proc. Amer. Math. Soc. 73 (1979), 121–125.CrossRefGoogle Scholar
[4]Schmidt, W. M.. On badly approximable numbers and certain games. Trans. Amer. Math. Soc. 123 (1966), 178–199.CrossRefGoogle Scholar
[5]Schmidt, W. M.. Diophantine Approximation, Springer-Verlag: Berlin-Heidelberg-New York, 1980.Google Scholar
[6]Walters, P.. An Introduction to Ergodic Theory, Springer-Verlag: Berlin-Heidelberg-New York, 1982.CrossRefGoogle Scholar