The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Ergodic Solenoidal Homology II: Density of Ergodic Solenoids


Vicente Muoz and Ricardo Prez Marco

Instituto de Ciencias Matemticas CSIC-UAM-UC3M-UCM,
 Serrano 113 bis, 28006 Madrid,
Facultad de Matem
ticas, Universidad Complutense de Madrid,
 Plaza de Ciencias 3, 28040 Madrid,

CNRS, LAGA UMR 7539, Universit
Paris XIII,
99 Avenue J.-B. Cl\'ement, 93430-Villetaneuse,


A measured solenoid is a laminated space endowed with a tranversal measure invariant by holonomy. A measured solenoid immersed in a smooth manifold produces a closed current (known as a generalized Ruelle-Sullivan current). Uniquely ergodic solenoids are those for which there is a unique (up to scalars) transversal measure. It is known that for any smooth manifold, any real homology class is represented by a uniquely ergodic solenoid. In this paper, we prove that the currents associated to uniquely ergodic solenoids are dense in the space of closed currents, therefore proving the abundance of such objects.

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