Symplectic analysis of dynamical systems with a small parameter. A new criterion for stabilization of homoclinic separatrices and its application

Autor: V. G. Samoilenko, A. K. Prikarpats'kyy, Yu. O. Mitropol'skii, I. O. Antonishin
Rok vydání: 1992
Předmět:
Zdroj: Ukrainian Mathematical Journal. 44:41-58
ISSN: 1573-9376
0041-5995
DOI: 10.1007/bf01062626
Popis: Adiabatic invariants of nonlinear dynamical autonomous and nonautonomous type systems on symplectic manifolds, particularly existence criteria for these systems and methods of constructing them explicitly, are studied. A thorough analysis of the phenomenon of the splitting of a homoclinic separatrix with a singular hyperbolic-type point is conducted, and a new, exact method of constructing an analogue of the Mel'nikov μ-function that yields necessary and sufficient transversality conditions which may be automatically generalized to the case of a dynamical system in ℝ n ,n e ℤ+, is suggested.
Databáze: OpenAIRE
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