Invariant vector fields and groupoids

2013/07/29 by Eugene Lerman, Lerman, Eugene
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1307.7733

15 pages. Comments and corrections appreciated (v2): example added (v3): partially re-written in response to referees' comments. Accepted for publication in IMRN

arxiv created 2014/09/08 · arxiv updated 2014/09/10

Abstract

We use the notion of isomorphism between two invariant vector fields to shed new light on the issue of linearization of an invariant vector field near a relative equilibrium. We argue that the notion is useful in understanding the passage from the space of invariant vector fields in a tube around a group orbit to the space invariant vector fields on a slice to the orbit. The notion comes from Hepworth's study of vector fields on stacks.

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