Bernold Fiedler, Bj?rn Sandstede, Arnd Scheel and Claudia Wulff

摘要

We consider a finite-dimensional, typically noncompact Riemannianmanifold $M$ with a differentiable proper action of a possiblynon-compact Lie group $G.$ We describe $G$-equivariant flows in atubular neighborhood $U$ of a relative equilibrium $Gcdot u_0,u_0inM$, with compact isotropy $H$ of $u_0,$ by a skew product flow$dot{g} = g {f a}(v),$ $dot{v} = arphi(v).$ Here $gin G, {f a}in {m alg}(G).$ Thevector $v$ is in a linear slice $V$ to the group action. The inducedlocal flow on $Gimes V$ is equivariant under the action of$(g_0,h)in Gimes H$ on $(g,v)in Gimes V,$ given by$(g_0,h)(g,v) = (g_0 gh^{-1},hv).$ The original flow on $U$ isequivalent to the induced flow on ${id}imes H$-orbits in $GimesV.$