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Ergodic solenoidal homology. II. Density of ergodic solenoids.

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Muñoz, Vicente and Pérez Marco, Ricardo (2009) Ergodic solenoidal homology. II. Density of ergodic solenoids. The Australian Journal of Mathematical Analysis and Applications, 6 (1). pp. 1-8. ISSN 1449-5910

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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.


Item Type:Article
Additional Information:

Special Issue in Honor of the 100th Anniversary of S.M. Ulam

Uncontrolled Keywords:Ruelle-Sullivan current; Solenoid; Ergodic theory
Subjects:Sciences > Mathematics > Topology
ID Code:20884
Deposited On:17 Apr 2013 12:58
Last Modified:19 Feb 2019 12:07

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