# Ergodic Measures for Sectional-Anosov Flows

### From NZJM

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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.

**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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