Dynamics of abelian subgroups of GL(n, C): a structure's Theorem

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dc.creatorAyadi, A.
dc.creatorMarzougui, H.
dc.date2005-01-10
dc.date.accessioned2026-07-07T06:24:13Z
dc.date.available2026-07-07T06:24:13Z
dc.descriptionIn this paper, we characterize the dynamic of every abelian subgroups $\mathcal{G}$ of GL($n$, $\mathbb{K}$), $\mathbb{K} = \mathbb{R}$ or $\mathbb{C}$. We show that there exists a $\mathcal{G}$-invariant, dense open set $U$ in $\mathbb{K}^{n}$ saturated by minimal orbits with $\mathbb{K}^{n}- U$ a union of at most $n$ $\mathcal{G}$-invariant vectorial subspaces of $\mathbb{K}^{n}$ of dimension $n-1$ or $n-2$ on $\mathbb{K}$. As a consequence, $\mathcal{G}$ has height at most $n$ and in particular it admits a minimal set in $\mathbb{K}^{n}-\{0\}$.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math/0501136
dc.identifierhttp://arxiv.org/abs/math/0501136
dc.identifierGeometriae Dedicata , vol. 116, Number 1 (2005), 111-127
dc.identifierdoi:10.1007/s10711-005-9007-2
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96467
dc.subjectDynamical Systems
dc.subjectGeometric Topology
dc.subject37C85
dc.titleDynamics of abelian subgroups of GL(n, C): a structure's Theorem
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