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:	Nonlinear system Transversality Dynamical systems theory General Mathematics Mathematical analysis Homoclinic orbit Type (model theory) Dynamical system Symplectic geometry Mathematics Symplectic manifold
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
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0870fd6e3def44e10bd0c865acad4c5a https://doi.org/10.1007/bf01062626 Zobrazit plný text záznamu Full text from SpringerLink