On ergodic averages for affine lattice actions on tori

Dani, S. G. ; Muralidharan, S. (1983) On ergodic averages for affine lattice actions on tori Monatshefte für Mathematik, 96 (1). pp. 17-28. ISSN 0026-9255

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Official URL: http://www.springerlink.com/content/x68p76358lg4g2...

Related URL: http://dx.doi.org/10.1007/BF01298931

Abstract

We prove that for a Zν-action on a torus as a group of affine transformations all the ergodic averages exist if and only if all the eigenvalues of the automorphism parts of all the affine transformations are roots of unity.

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