Timeline for What does the Jacobian of a vector field at an equilibrium tell you about local behavior of integral curves when the Jacobian is not a stable?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 31, 2023 at 21:30 | vote | accept | Spencer Kraisler | ||
| Jul 31, 2023 at 18:36 | comment | added | Martin M. W. | In your case there exists a 1-dimensional center manifold (don't assume uniqueness, though!) through the equilibrium, and in a neighborhood of the equilibrium trajectories will be attracted to this 1D manifold. The issue is that the dynamics on the center manifold could be attracting, repelling, or (as in the first vector field above) a combination. | |
| Jul 31, 2023 at 17:17 | comment | added | Spencer Kraisler | Doesn't center manifold theorems give us information about the local behavior? | |
| Jul 30, 2023 at 21:27 | history | edited | Martin M. W. | CC BY-SA 4.0 |
added 48 characters in body
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| Jul 30, 2023 at 21:16 | history | answered | Martin M. W. | CC BY-SA 4.0 |