On the Dynamics of G-Solenoids. Applications to Delone Sets

dc.creatorBenedetti, Riccardo
dc.creatorGambaudo, Jean-Marc
dc.date2002-08-30
dc.date.accessioned2026-07-07T04:50:28Z
dc.date.available2026-07-07T04:50:28Z
dc.descriptionA G-solenoid is a laminated space whose leaves are copies of a single Lie group G, and whose transversals are totally disconnected sets. It inherits a G-action and can be considered as dynamical system. Free Z^d-actions on the Cantor set as well as a large class of tiling spaces possess such a structure of G-solenoid. We show that a G-solenoid can be seen as a projective limit of branched manifolds modeled on G. This allows us to give a topological description of the transverse invariant measures associated with a G-solenoid in terms of a positive cone in the projective limit of the dim(G)-homology groups of these branched manifolds. In particular we exhibit a simple criterion implying unique ergodicity. A particular attention is paid to the case when the Lie group $G$ is the group of affine orientation preserving isometries of the Euclidean space or its subgroup of translations.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0208243
dc.identifierhttp://arxiv.org/abs/math/0208243
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64808
dc.subjectDynamical Systems
dc.subject37C40, 22F30, 52C22
dc.titleOn the Dynamics of G-Solenoids. Applications to Delone Sets
dc.typetext

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