The Poincare-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I

• Date: 1993
• Main Authors: Prykarpatsky, A. K., Samoilenko, A. M., Timchishin, O. Ya., Прикарпатський, А. К., Самойленко, А. М., Тимчишин, О. Ф.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5975
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

On the basis of the geometric ideas of Poincaré and Mel'nikov, we study sufficient criteria of the transversal splitting of heteroclinic separatrix manifolds of slowly perturbed nonlinear dynamical systems with a small parameter. An example of adiabatic invariance breakdown is considered fo...