Topographic Poincar\'e systems and comparison systems of small and high orders

M. V. Shamolin

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 187 (2020), pp. 50-67.

Résumé

On this work, we consider some qualitative questions of the theory of ordinary differential equations, on whose solutions a study of a series of dynamical systems depends. An elementary survey is given for such problems as qualitative questions of the theory of topographic Poincaré systems and more general comparison systems; problems of the existence and uniqueness of trajectories having infinitely distant points for flat systems as limit sets; elements of the qualitative theory of monotone vector fields.

Détail

Keywords: dynamical system, topographic Poincaré system, comparison system, integrability.

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