It is shown that two-degree-of-freedom Hamiltonian systems of the billiard type are equivalent to adiabatically varying one-degree-of-freedom Hamiltonian systems for solutions staying near the boundary. Under some nondegeneracy conditions such systems possess a large set of quasiperiodic solutions filling out two-dimensional invariant tori. The latter separate the extended phase space into layers providing stability for all time. The result is illustrated on a few examples.
|Original language||English (US)|
|Number of pages||4|
|Journal||Physical review letters|
|State||Published - Nov 30 1998|
ASJC Scopus subject areas
- Physics and Astronomy(all)