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Density of mild mixing property for vertical flows of Abelian differentials

Author(s): Krzysztof Fraczek
Journal: Proc. Amer. Math. Soc. 137 (2009), 4129-4142.
MSC (2000): Primary 37A10, 37E35; Secondary 30F30
Posted: July 1, 2009
MathSciNet review: 2538574
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Abstract | References | Similar articles | Additional information

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 Torun, Poland - and - Institute of Mathematics, Polish Academy of Science, ul. Sniadeckich 8, 00-956 Warszawa, Poland
Email: fraczek@mat.uni.torun.pl

DOI: 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
Posted: 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
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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