Publication: Ergodic solenoidal homology. II. Density of ergodic solenoids.
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Publication Date
2009
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Austral Internet Publishing
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Abstract
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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Special Issue in Honor of the 100th Anniversary of S.M. Ulam
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