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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Density of mild mixing property for vertical flows of Abelian differentials


Author: Krzysztof Fraczek
Journal: Proc. Amer. Math. Soc. 137 (2009), 4129-4142
MSC (2000): Primary 37A10, 37E35; Secondary 30F30
Published electronically: July 1, 2009
MathSciNet review: 2538574
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Abstract: We prove that if $ g\geq 2$, then the set of all Abelian differentials $ (M,\omega)$ for which the vertical flow is mildly mixing is dense in every stratum of the moduli space $ \mathcal{H}_g$. The proof is based on a sufficient condition due to Frączek, Lemańczyk, and Lesigne guaranteeing mild mixing property of certain special flows over irrational rotations.


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Additional Information

Krzysztof Fraczek
Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland – and – Institute of Mathematics, Polish Academy of Science, ul. Śniadeckich 8, 00-956 Warszawa, Poland
Email: fraczek@mat.uni.torun.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10025-4
PII: S 0002-9939(09)10025-4
Keywords: Mild mixing property, measure--preserving flows, direction flows, Abelian differentials
Received by editor(s): November 19, 2008
Received by editor(s) in revised form: March 19, 2009
Published electronically: July 1, 2009
Additional Notes: This research was partially supported by MNiSzW grant NN201 384834 and the Marie Curie “Transfer of Knowledge” program, project MTKD-CT-2005-030042 (TODEQ)
Communicated by: Bryna Kra
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.