5
votes
Accepted
Exact solution to a periodic linear ODE sought
Rather incredibly, your (corrected) system does have a closed-form solution, which I found with Maple's help.
$$ x(t) = 1+4\,\cos \left( 2\,t \right) +3\,\sqrt {8\,\cos \left( 2\,t \right) +
17}$$
$y(...
- 54.2k
3
votes
An elliptic operator whose corresponding symbol Hamiltonian vector field has an isolated periodic orbit
I'm going to assume that you want an isolated periodic orbit on some fixed energy level. Pick your favorite Riemannian manifold $(M,g)$ such that there is an isolated closed geodesic. Then, the ...
- 3,020
2
votes
Accepted
On properties of Besse spheres
It so happens I recently read this same passage in Besse's book. I am no expert, but here is how I understand it.
Question 1. Let $p,q \in \mathbf{S}^2$ be two arbitrary points, and $\eta: [0,L] \to \...
- 5,038
2
votes
Stable periodic orbits for three equal masses
The proposer gives as their definition of stability the standard notion
of Lyapunov stability. Unfortunately, there are no known solutions for the planar or spatial three-body problem which are ...
- 8,336
1
vote
Floquet coefficients under time change
I may have a computation free answer to my own question. If we take a periodic orbit and define a section S. This allows to introduce a poincare return map P. Then, it is well known that the ...
- 41
1
vote
Floquet coefficients under time change
It is better to see the connection on the level of semiflows generated by the equations. Namely, let $\varphi^{t}$ be the semiflow generated by $(1)$ and $\psi^{t}$ be the semiflow generated by $(2)$, ...
- 798
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