Quasiperiodic Motion in the Hamiltonian Systems of the Billiard Type

Journal Article · Sat Oct 31 23:00:00 EST 1998 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.81.4839· OSTI ID:670232

Zharnitsky, V ^[1]

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1. Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912 (United States)

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. {copyright} {ital 1998} {ital The American Physical Society}

• OSTI ID: 670232
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 22 Vol. 81; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ADIABATIC INVARIANCE
CLASSICAL MECHANICS
HAMILTONIAN FUNCTION
PHASE SPACE
QUANTUM MECHANICS
SEMICLASSICAL APPROXIMATION