Talk:Heteroclinic orbit

Title
I would like to change the title of this page to "Heteroclinic orbit" which I think is a more generic name. Does anyone object?


 * I support a move to "Heteroclinic orbit" (have never heard the word "heteroclinic path", dynamical systems and symplectic geometry people I know always use "orbit"), but oppose a move to "heteroclinic cycle", which is something different. Kusma (討論) 15:11, 12 May 2006 (UTC)


 * Sorry my mistake I meant orbit not cycle - a dumb typo. I'll change it. Mathmoclaire
 * Support. Google shows 32 hits for "heteroclinic path" and over 15,000 for "heteroclinic orbit". Kafziel 17:57, 12 May 2006 (UTC)
 * Done. &mdash; Nightst a  llion  (?) 06:59, 17 May 2006 (UTC)

Error?
I think for an orbit to be heteroclinic, it must join the stable and unstable manifolds. The article definition does not even begin to attempt to explain this. Does WP have any articles that explain the stable manifolds and unstable manifolds of a flow (aside from Anosov flow, which is far too technical)? I'll try to fix this up myself, if I get the chance. linas 14:48, 7 June 2006 (UTC)


 * Yes, that's correct, but it is implied by the definition given here (ie that as t->infty the trajectory -> x1 meaning it is contained in it's stable manifold. I've added a line saying as much. Is that clear? Mathmoclaire 16:57, 8 June 2006 (UTC)


 * Yes, better, thanks.linas 20:01, 10 June 2006 (UTC)

I have an issue with the figure (top right) of the phase portrait of the pendulum. It describes the orbit from (-pi,0) to (pi,0) as heteroclinic, but considered in the natural (cylindrical) manifold of a pendulum, these two points are the same, so I would consider this a homoclinic orbit. Agree? — Preceding unsigned comment added by 128.30.7.10 (talk) 15:48, 21 July 2011 (UTC)