On the regularity of integrable conformal structures invariant under Anosov systems

Rafael De La Llave; Victoria Sadovskaya

doi:10.3934/dcds.2005.12.377

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2005, Volume 12, Issue 3: 377-385. Doi: 10.3934/dcds.2005.12.377

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On the regularity of integrable conformal structures invariant under Anosov systems

Rafael De La Llave^1, and
Victoria Sadovskaya^2,

1.
Department of Mathematics, 1 University Station C1200, University of Texas, Austin, TX 78712
2.
Department of Mathematics and Statistics, ILB 325, University of South Alabama, Mobile, AL 36688

Received: September 30, 2003

Revised: July 31, 2004

Published: March 2005

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Abstract

We consider conformal structures invariant under a volume-preserving Anosov system. We show that if such a structure is in $L^p$ for sufficiently large $p$, then it is continuous.

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Mathematics Subject Classification: 37D20, 37F15, 30C65, 42B20.

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