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February  2006, 15(1): 193-196. doi: 10.3934/dcds.2006.15.193

Cohomology free systems and the first Betti number

Federico Rodriguez Hertz 1, and  Jana Rodriguez Hertz 1,

1. 

LHE - IMERL, Facultad de Ingeniería - Universidad de la República, Julio Herrera y Reissig 565, CP 11300, Montevideo, Uruguay, Uruguay

Received  November 2004 Revised  November 2005 Published  February 2006

We prove that a cohomology free flow on a manifold $M$ fibers over a diophantine translation on $\T^{\beta_1}$ where $\beta_1$ is the first Betti number of $M$.
Keywords: Cohomolgy equation, tori., diophantine vector field.
Mathematics Subject Classification: Primary: 37C15, 37C55; Secondary: 37C4.
Citation: Federico Rodriguez Hertz, Jana Rodriguez Hertz. Cohomology free systems and the first Betti number. Discrete & Continuous Dynamical Systems, 2006, 15 (1) : 193-196. doi: 10.3934/dcds.2006.15.193
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