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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2020, Volume 187, Pages 50–67 (Mi into732)  

Topographic Poincaré systems and comparison systems of small and high orders

M. V. Shamolin

Lomonosov Moscow State University

Abstract: 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.

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

DOI: https://doi.org/10.36535/0233-6723-2020-187-50-67

Full text: PDF file (288 kB)
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UDC: 517, 531.01
MSC: 34Cxx, 70Cxx

Citation: M. V. Shamolin, “Topographic Poincaré systems and comparison systems of small and high orders”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 187, VINITI, Moscow, 2020, 50–67

Citation in format AMSBIB
\Bibitem{Sha20}
\by M.~V.~Shamolin
\paper Topographic Poincar\'e systems and comparison systems of small and high orders
\inbook Geometry and Mechanics
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 187
\pages 50--67
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into732}
\crossref{https://doi.org/10.36535/0233-6723-2020-187-50-67}


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