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Minimal non-ergodic directions on genus-2 translation surfaces

Published online by Cambridge University Press:  17 March 2006

YITWAH CHEUNG  and
HOWARD MASUR
YITWAH CHEUNG
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Avenue, Evanston, IL 60208-2730, USA (e-mail: yitwah@math.northwestern.edu)
HOWARD MASUR
Affiliation:
Department of Mathematics, University of Illinois at Chicago, 851 South Morgan, Chicago, IL 60607-7045, USA (e-mail: masur@math.uic.edu)
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Abstract

It is well known that on any Veech surface, the dynamics in any minimal direction is uniquely ergodic. In this paper it is shown that for any genus-2 translation surface which is not a Veech surface there are uncountably many minimal but not uniquely ergodic directions. The theorem can be applied to certain billiard tables.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 2 , April 2006 , pp. 341 - 351
Copyright
2006 Cambridge University Press

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