Timeline for Global stability for dynamical systems in $R^n$
Current License: CC BY-SA 2.5
5 events
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| May 19, 2010 at 13:50 | comment | added | Martin M. W. | Good question, I don't know the answer for polynomials. If I were looking for a polynomial counterexample, I might start in dimension n=4, and try to write down a system where the dynamics were (a) an attracting fixed point at the origin; (b) an irrational rotation flow on a 2-torus embedded on the unit sphere; and (c) outside of the 2-torus and the origin, the distance to the origin would always decrease along orbits. But I don't really know if this approach would work. | |
| May 19, 2010 at 7:26 | comment | added | Guy Katriel | Thank you, this is very interesting. Let me add that my question is motivated by particular systems of ODE's for which one can show that assumptions (1)-(3) hold, and one would like to prove global stability. In these systems, the ODE's are polynomial ones. So I wonder if it is possible to get a positive answer by restricting the class of vector fields to polynomial ones. Since a "plugging" construction cannot be performed with polynomial vector fields, maybe there is a chance.. | |
| May 19, 2010 at 6:58 | vote | accept | Guy Katriel | ||
| May 19, 2010 at 6:58 | |||||
| May 19, 2010 at 6:57 | vote | accept | Guy Katriel | ||
| May 19, 2010 at 6:57 | |||||
| May 18, 2010 at 23:44 | history | answered | Martin M. W. | CC BY-SA 2.5 |