Timeline for Holomorphic vector fields with a non-degenerate isolated zero
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 23, 2020 at 16:50 | vote | accept | aglearner | ||
| Oct 23, 2020 at 15:14 | comment | added | Ben McKay | The dynamics of a linear vector field with resonances are going to repeat for infinitely many values of complex time, but when you throw in some resonances, you break that, so you can't get back to the linear case, since the linearization is an invariant. | |
| Oct 23, 2020 at 15:04 | comment | added | Ben McKay | If you rescale a resonant vector field, you get resonances with eigenvalues as large or as small as you like. | |
| Oct 23, 2020 at 14:59 | comment | added | Ben McKay | Sorry, I gave the result for maps, not for vector fields. Here is the correct version for vector fields. | |
| Oct 23, 2020 at 14:59 | history | edited | Ben McKay | CC BY-SA 4.0 |
Gave the result for vector fields; previously I had it for maps.
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| Oct 23, 2020 at 12:58 | comment | added | aglearner | I am curious, in the case when all the eigenvalues of $A$ are smaller than $1$ in modulus, can it happen (say when there are resonants) that the mapping is not holomorphically conjugate to a linear one in a small neighbourhood of $0$? | |
| Oct 21, 2020 at 15:58 | history | answered | Ben McKay | CC BY-SA 4.0 |