Quasienergy intergral for canonical maps

Journal Article · Sat Nov 01 00:00:00 EST 1986 · Theor. Math. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01118153· OSTI ID:6750111

Sokolov, V V

Canonical (area-preserving) maps of the phase plane of action-angle variables whose coefficients do not depend explicitly on the number of mapping steps are considered. Just as the absence of an explicit time dependence of the coefficients of a canonical system of differential equations leads to energy conservation, such maps may have an integral of the motion - called a quasienergy integral. It is shown that such an integral can be constructed in the form of a series of analytic functions, a perturbation-theory series, and the superconvergent series of Kolmogorov-Arnol'd-Moser (KAM) theory. These series converge only in limited regions of the phase plane, and their sums have simple poles at fixed (resonance) points of the map. For a sufficiently small perturbation constant g, it is possible to find approximate regular expressions for the quasienergy near any given resonance with any finite accuracy in g. The regions of applicability of the obtained expressions overlap, and this makes it possible to construct at small g an approximate phase portrait of the map on the complete phase plane.

• Research Organization: Institute of Nuclear Physics, Siberian Acad. of Sci.
• OSTI ID: 6750111
• Journal Information: Theor. Math. Phys.; (United States), Vol. 67:2
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
CANONICAL TRANSFORMATIONS
INTEGRALS
MATHEMATICAL MANIFOLDS
CONVERGENCE
HAMILTONIANS
KOLMOGOROV EQUATION
PERTURBATION THEORY
PHASE SPACE
POISSON EQUATION
SERIES EXPANSION
TIME DEPENDENCE
TOPOLOGY
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SPACE
TRANSFORMATIONS
645400* - High Energy Physics- Field Theory