Simplex analysis of dynamical systems with a perturbation. New criteria of stabilization of a homoclinic separatrix and its use

• Date: 1992
• Main Authors: Mitropolsky , Yu. O., Antonishin , I. O., Prikarpatsky , A. K., Samoilenko , V. G., Митропольський , Ю. О., Антонишин , І. О., Прикарпатський , А. К., Самойленко , В. Г.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 1992
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2319
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study adiabatic invariants of nonlinear dynamical systems of autonomous and nonautonomous type on symplectic manifolds, and, in particular, give criteria for the existence of such invariants and methods for constructing them explicitly. We make a thorough analysis of the phenomena of splitting of...