A nonintegrability criterion for adiabatic systems. (English) Zbl 1140.70007
The authors study a system of ordinary differential equations
\[ \dot q=\partial H / \partial p (p,q,z), \quad \dot p= -\partial H / \partial q (p,q,z), \quad \dot z =\varepsilon, \]
arising from plasma physics. A sufficient non-integrability condition for this system is formulated in terms of the “frozen” system corresponding to the limit case \(\varepsilon=0\) and its homoclinic loops. As application, the Hamiltonian \(H= 1/2 p^2 +V(x,z)\) is considered for some special polynomial potential \(V\) of fourth degree.
\[ \dot q=\partial H / \partial p (p,q,z), \quad \dot p= -\partial H / \partial q (p,q,z), \quad \dot z =\varepsilon, \]
arising from plasma physics. A sufficient non-integrability condition for this system is formulated in terms of the “frozen” system corresponding to the limit case \(\varepsilon=0\) and its homoclinic loops. As application, the Hamiltonian \(H= 1/2 p^2 +V(x,z)\) is considered for some special polynomial potential \(V\) of fourth degree.
Reviewer: Alexei Tsygvintsev (Lyon)
MSC:
| 70H07 | Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics |
| 76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
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