Stable and Unstable manifolds of saddle points, vortex, center?

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I was reading this article on the stable and unstable manifolds of an invariant set - http://www.cnbc.cmu.edu/~bard/xppfast/lin2d.html.



It is intutitve that the stable manifold for the stable node (by seeing the figure)is the whole plane but how the unstable manifold of the stable node is the node itself?



Also how to understand the stable and unstable manifolds of the center and the vortex?




manifolds dynamical-systems intuition




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  • Oh I meant for stable node, let me edit! thanks for pointing out
    – BAYMAX
    Jul 28 at 7:03










  • Also the stable manifold must be a span of the eigenvectors of the negative eigenvalue right?
    – BAYMAX
    Jul 28 at 7:06











  • Yes, that's O.K.
    – user539887
    Jul 28 at 7:06






  • 1




    The unstable manifold of the stable node is the node itself because the only point which tends to the node as time goes to negative infinity is just the node (the same is true for the stable vortex).
    – user539887
    Jul 28 at 7:11














up vote
0
down vote

favorite












I was reading this article on the stable and unstable manifolds of an invariant set - http://www.cnbc.cmu.edu/~bard/xppfast/lin2d.html.



It is intutitve that the stable manifold for the stable node (by seeing the figure)is the whole plane but how the unstable manifold of the stable node is the node itself?



Also how to understand the stable and unstable manifolds of the center and the vortex?




manifolds dynamical-systems intuition




share|cite|improve this question





















  • Oh I meant for stable node, let me edit! thanks for pointing out
    – BAYMAX
    Jul 28 at 7:03










  • Also the stable manifold must be a span of the eigenvectors of the negative eigenvalue right?
    – BAYMAX
    Jul 28 at 7:06











  • Yes, that's O.K.
    – user539887
    Jul 28 at 7:06






  • 1




    The unstable manifold of the stable node is the node itself because the only point which tends to the node as time goes to negative infinity is just the node (the same is true for the stable vortex).
    – user539887
    Jul 28 at 7:11












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I was reading this article on the stable and unstable manifolds of an invariant set - http://www.cnbc.cmu.edu/~bard/xppfast/lin2d.html.



It is intutitve that the stable manifold for the stable node (by seeing the figure)is the whole plane but how the unstable manifold of the stable node is the node itself?



Also how to understand the stable and unstable manifolds of the center and the vortex?




manifolds dynamical-systems intuition




share|cite|improve this question













I was reading this article on the stable and unstable manifolds of an invariant set - http://www.cnbc.cmu.edu/~bard/xppfast/lin2d.html.



It is intutitve that the stable manifold for the stable node (by seeing the figure)is the whole plane but how the unstable manifold of the stable node is the node itself?



Also how to understand the stable and unstable manifolds of the center and the vortex?





manifolds dynamical-systems intuition





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 28 at 7:04
























asked Jul 28 at 6:32









BAYMAX

2,43121021




2,43121021











  • Oh I meant for stable node, let me edit! thanks for pointing out
    – BAYMAX
    Jul 28 at 7:03










  • Also the stable manifold must be a span of the eigenvectors of the negative eigenvalue right?
    – BAYMAX
    Jul 28 at 7:06











  • Yes, that's O.K.
    – user539887
    Jul 28 at 7:06






  • 1




    The unstable manifold of the stable node is the node itself because the only point which tends to the node as time goes to negative infinity is just the node (the same is true for the stable vortex).
    – user539887
    Jul 28 at 7:11
















  • Oh I meant for stable node, let me edit! thanks for pointing out
    – BAYMAX
    Jul 28 at 7:03










  • Also the stable manifold must be a span of the eigenvectors of the negative eigenvalue right?
    – BAYMAX
    Jul 28 at 7:06











  • Yes, that's O.K.
    – user539887
    Jul 28 at 7:06






  • 1




    The unstable manifold of the stable node is the node itself because the only point which tends to the node as time goes to negative infinity is just the node (the same is true for the stable vortex).
    – user539887
    Jul 28 at 7:11















Oh I meant for stable node, let me edit! thanks for pointing out
– BAYMAX
Jul 28 at 7:03




Oh I meant for stable node, let me edit! thanks for pointing out
– BAYMAX
Jul 28 at 7:03












Also the stable manifold must be a span of the eigenvectors of the negative eigenvalue right?
– BAYMAX
Jul 28 at 7:06





Also the stable manifold must be a span of the eigenvectors of the negative eigenvalue right?
– BAYMAX
Jul 28 at 7:06













Yes, that's O.K.
– user539887
Jul 28 at 7:06




Yes, that's O.K.
– user539887
Jul 28 at 7:06




1




1




The unstable manifold of the stable node is the node itself because the only point which tends to the node as time goes to negative infinity is just the node (the same is true for the stable vortex).
– user539887
Jul 28 at 7:11




The unstable manifold of the stable node is the node itself because the only point which tends to the node as time goes to negative infinity is just the node (the same is true for the stable vortex).
– user539887
Jul 28 at 7:11















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