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Results tagged with differential-equations
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user 75853
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
1
vote
When is a limit cycle generated by a Hamiltonian oval stable?
Well, it looks like this is simply a matter of a Poincare map. If you look at a proof of Pontryagin's criterion, it turns out that the integral $I(t)$ is the first derivative of the Poincare map with …
- 460
1
vote
A special non vanishing vector field on $S^{3}$
I believe the answer to both of your questions is ''yes".
Any real-analytic vector field on $\mathbb{S}^2$ that has a
center singularity can be lifted to a one-parameter family of
non-vanishing vect …
- 460
5
votes
Accepted
Two limit cycles which lie on the same leaf
Possibly a very "brute force" approach could be the following. Take an non-singular algebraic curve $H(x,y)=0$ given by a polynomial $H(x,y)$ with real coefficients that has at least two ovals in the …
- 460
2
votes
The type of a Riemann surface arising from a polynomial vector field
Well, in general not too much can be said without further information. For sure the leaf has a nontrivial fundamental group, so not an elliptic Reiamann surface (i.e. a Riemann sphere). But it could …
- 460