Timeline for Periodic orbits of Hamiltonian systems
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2012 at 10:43 | history | edited | HorizonsMaths | CC BY-SA 3.0 |
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| Jan 19, 2012 at 9:49 | comment | added | HorizonsMaths | Thanks for the precision. I want conditions for the existence of a T-periodic orbit having a prescribed period and whose coordinates are non constants | |
| Jan 19, 2012 at 9:21 | comment | added | Pietro Majer | so, you want conditions on $V$ that ensure the existence of a T-periodic orbit with non-constant coordinates for any prescribed period T, or would it be OK the existence of just a periodic orbit with non-constant coordinates? | |
| Jan 19, 2012 at 9:06 | comment | added | HorizonsMaths | I'm actually refering to those assumptions made by Rabinowitz to prove what I just claimed! | |
| Jan 19, 2012 at 3:02 | comment | added | Mike Usher | Maybe I'm misunderstanding, but I don't see how you get a nonconstant periodic orbit for an arbitrary period. For instance if you set $V'(x)=x$ then all the periodic orbits seem to have period $2\pi$. More generally, assuming that $V'$ is Lipschitz, the Yorke estimate (applied to the corresponding first-order system on $R^{2N}$) gives an explicit positive lower bound for the minimal period of a periodic orbit. Am I misinterpreting what you wrote? Or maybe your "natural assumptions" involved $V'$ growing faster than linearly, though this would seem a bit unphysical... | |
| Jan 18, 2012 at 19:56 | history | asked | HorizonsMaths | CC BY-SA 3.0 |