Computation of stable manifold

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I've been reading a bit around on computation of unstable manifold, which seem to be a big area of research, however no one ever mentions computation of the stable manifold.



Is this because you just reverse time, and then the stable manifold becomes the unstable one, thus computational methods of unstable manifolds also covers computation of stable ones?



Regards,




manifolds dynamical-systems




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  • Yeah, even one of the most comprehensive surveys on this topic (see link in this answer) "A survey of methods for computing (un)stable manifolds of vector fields" has this kind of word-play that suggests that these problems are to some extent the same. The caveat is only when an unstable manifold of transformed system escapes to infinity.
    – Evgeny
    Jul 16 at 19:52















up vote
0
down vote

favorite












I've been reading a bit around on computation of unstable manifold, which seem to be a big area of research, however no one ever mentions computation of the stable manifold.



Is this because you just reverse time, and then the stable manifold becomes the unstable one, thus computational methods of unstable manifolds also covers computation of stable ones?



Regards,




manifolds dynamical-systems




share|cite|improve this question



















  • Yeah, even one of the most comprehensive surveys on this topic (see link in this answer) "A survey of methods for computing (un)stable manifolds of vector fields" has this kind of word-play that suggests that these problems are to some extent the same. The caveat is only when an unstable manifold of transformed system escapes to infinity.
    – Evgeny
    Jul 16 at 19:52













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I've been reading a bit around on computation of unstable manifold, which seem to be a big area of research, however no one ever mentions computation of the stable manifold.



Is this because you just reverse time, and then the stable manifold becomes the unstable one, thus computational methods of unstable manifolds also covers computation of stable ones?



Regards,




manifolds dynamical-systems




share|cite|improve this question











I've been reading a bit around on computation of unstable manifold, which seem to be a big area of research, however no one ever mentions computation of the stable manifold.



Is this because you just reverse time, and then the stable manifold becomes the unstable one, thus computational methods of unstable manifolds also covers computation of stable ones?



Regards,





manifolds dynamical-systems





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 15 at 10:46









1233023

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1398











  • Yeah, even one of the most comprehensive surveys on this topic (see link in this answer) "A survey of methods for computing (un)stable manifolds of vector fields" has this kind of word-play that suggests that these problems are to some extent the same. The caveat is only when an unstable manifold of transformed system escapes to infinity.
    – Evgeny
    Jul 16 at 19:52

















  • Yeah, even one of the most comprehensive surveys on this topic (see link in this answer) "A survey of methods for computing (un)stable manifolds of vector fields" has this kind of word-play that suggests that these problems are to some extent the same. The caveat is only when an unstable manifold of transformed system escapes to infinity.
    – Evgeny
    Jul 16 at 19:52
















Yeah, even one of the most comprehensive surveys on this topic (see link in this answer) "A survey of methods for computing (un)stable manifolds of vector fields" has this kind of word-play that suggests that these problems are to some extent the same. The caveat is only when an unstable manifold of transformed system escapes to infinity.
– Evgeny
Jul 16 at 19:52





Yeah, even one of the most comprehensive surveys on this topic (see link in this answer) "A survey of methods for computing (un)stable manifolds of vector fields" has this kind of word-play that suggests that these problems are to some extent the same. The caveat is only when an unstable manifold of transformed system escapes to infinity.
– Evgeny
Jul 16 at 19:52











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Stable manifolds are, well, stable under the phase-space flow. Thus, in the most simple case, all you need to do is to integrate forwards in time when you are in the vicinity and you’ll obtain the stable manifold. In some cases (e.g., a quasiperiodic attractor), things may be a bit more difficult, but the gist stays the same.






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  • Thank you for your reply.
    – 1233023
    Jul 16 at 9:31










  • If you integrate trajectories in the vicinity of a saddle, after some time it traces out something very close to a part of unstable manifold :)
    – Evgeny
    Jul 16 at 19:48










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted










Stable manifolds are, well, stable under the phase-space flow. Thus, in the most simple case, all you need to do is to integrate forwards in time when you are in the vicinity and you’ll obtain the stable manifold. In some cases (e.g., a quasiperiodic attractor), things may be a bit more difficult, but the gist stays the same.






share|cite|improve this answer





















  • Thank you for your reply.
    – 1233023
    Jul 16 at 9:31










  • If you integrate trajectories in the vicinity of a saddle, after some time it traces out something very close to a part of unstable manifold :)
    – Evgeny
    Jul 16 at 19:48














up vote
1
down vote



accepted










Stable manifolds are, well, stable under the phase-space flow. Thus, in the most simple case, all you need to do is to integrate forwards in time when you are in the vicinity and you’ll obtain the stable manifold. In some cases (e.g., a quasiperiodic attractor), things may be a bit more difficult, but the gist stays the same.






share|cite|improve this answer





















  • Thank you for your reply.
    – 1233023
    Jul 16 at 9:31










  • If you integrate trajectories in the vicinity of a saddle, after some time it traces out something very close to a part of unstable manifold :)
    – Evgeny
    Jul 16 at 19:48












up vote
1
down vote



accepted







up vote
1
down vote



accepted






Stable manifolds are, well, stable under the phase-space flow. Thus, in the most simple case, all you need to do is to integrate forwards in time when you are in the vicinity and you’ll obtain the stable manifold. In some cases (e.g., a quasiperiodic attractor), things may be a bit more difficult, but the gist stays the same.






share|cite|improve this answer













Stable manifolds are, well, stable under the phase-space flow. Thus, in the most simple case, all you need to do is to integrate forwards in time when you are in the vicinity and you’ll obtain the stable manifold. In some cases (e.g., a quasiperiodic attractor), things may be a bit more difficult, but the gist stays the same.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Jul 15 at 21:07









Wrzlprmft

2,76611133




2,76611133











  • Thank you for your reply.
    – 1233023
    Jul 16 at 9:31










  • If you integrate trajectories in the vicinity of a saddle, after some time it traces out something very close to a part of unstable manifold :)
    – Evgeny
    Jul 16 at 19:48
















  • Thank you for your reply.
    – 1233023
    Jul 16 at 9:31










  • If you integrate trajectories in the vicinity of a saddle, after some time it traces out something very close to a part of unstable manifold :)
    – Evgeny
    Jul 16 at 19:48















Thank you for your reply.
– 1233023
Jul 16 at 9:31




Thank you for your reply.
– 1233023
Jul 16 at 9:31












If you integrate trajectories in the vicinity of a saddle, after some time it traces out something very close to a part of unstable manifold :)
– Evgeny
Jul 16 at 19:48




If you integrate trajectories in the vicinity of a saddle, after some time it traces out something very close to a part of unstable manifold :)
– Evgeny
Jul 16 at 19:48












 

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