Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with integrable-systems
Search options not deleted
user 97098
Liouville integrability means that there exists a regular foliation of the phase space by invariant manifolds such that the Hamiltonian vector fields associated to the invariants of the foliation span the tangent distribution: there exists a maximal set of Poisson-commuting invariants in phase space. May be used more broadly for systems possessing simple analytic solutions.
2
votes
1
answer
82
views
integrability and area-preservation property of dynamical systems
Suppose we have a map defined on a plane, $x_{1}=f(x_{0})$, where $x \in \mathbb{R}^{2}$. Assume it is integable: there exists a function $I$ of the phase space variable $x$ such that $I(x)=I(f(x))$. …
- 331
3
votes
0
answers
125
views
How are action variables linked to first integrals of a Hamiltonian?
Suppose I have an integrable Hamiltonian system $H(q_{1}, p_{1},..., q_{n}, p_{n})$, with first integrals $F_{1} = H, F_{2},..., F_{n}$. Excluding certain singular level sets (i.e. separatrices), one …
- 331
2
votes
0
answers
131
views
Are the following action-angle variables correct for the Hamiltonian $H = \sqrt{p}f(q)$? [closed]
Suppose I have a Hamiltonian $H=H(p,q)=H(p,q+1)$ defined on a cylinder $\mathbb{T} \times \mathbb{R}^{+}$, such that $$H(p,q) = \sqrt{p}f(q)$$ where $f(q)=f(q+1)>0$ is a periodic function of $q$, so t …
- 331
1
vote
0
answers
52
views
Example of an adiabatically perturbed integrable 2 d.o.f. Hamiltonian?
Consider the following (classical) Hamiltonian system: $H(u,v,p,q, \tau)$, where $(u,v)$ and $(p,q)$ are conjugated variables and $\tau = \epsilon t$ is a slowly varying parameter, $0 < \epsilon << 1$ …
- 331