Ergodic Measures for Sectional-Anosov Flows

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New Zealand Journal of Mathematics

Vol. 46, (2016), Pages 129-134


C.A. Morales

Instituto de Matematica

Universidade Federal do Rio de Janeiro

P. O. Box 68530 21945-970

Rio de Janeiro

Brazil.

mailto:morales@impa.br






Abstract Let X be a sectional-Anosov flow. We prove that if the ergodic measures of X are dense in the set of the invariant ones, then the closure of the periodic orbits of X is a homoclinic class. In particular, every Venice mask exhibits an invariant measure which cannot be approximated by ergodic ones.

Keywords Sectional-Anosov flow, Periodic Orbits, Transitive.

Classification (MSC2000) Primary 54H20, Secondary 49J53.

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