Ergodic Solenoidal Homology II:
Density of Ergodic Solenoids
Ergodic Solenoidal Homology II: Density of Ergodic Solenoids
Vicente Muñoz and Ricardo Pérez Marco
Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM,
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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