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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 Hepworths study of vector fields on stacks.
This paper describes a relationship between essentially finite groupoids and 2-vector spaces. In particular, we show to construct 2-vector spaces of Vect-valued presheaves on such groupoids. We define 2-linear maps corresponding to functors between g
For a smooth near identity map, we introduce the notion of an interpolating vector field written in terms of iterates of the map. Our construction is based on Lagrangian interpolation and provides an explicit expressions for autonomous vector fields
In this work a theorical framework to apply the Poincare compactification technique to locally Lipschitz continuous vector fields is developed. It is proved that these vectors fields are compactifiable in the n-dimensional sphere, though the compacti
Unless another thing is stated one works in the $C^infty$ category and manifolds have empty boundary. Let $X$ and $Y$ be vector fields on a manifold $M$. We say that $Y$ tracks $X$ if $[Y,X]=fX$ for some continuous function $fcolon Mrightarrowmathbb
We study the number and distribution of the limit cycles of a planar vector field whose component functions are random polynomials. We prove a lower bound on the average number of limit cycles when the random polynomials are sampled from the Kostlan-