Review of research on the qualitative theory of differential equations at St. Petersburg university. I: Stable periodic points of diffeomorphisms with homoclinic points and systems with weakly hyperbolic invariant sets

DOI10.1134/S106345412470002XMaRDI QIDQ6638395

T. E. Zvyagintseva, E. V. Vasil'eva, Yu. A. Iljin, Nikita Begun

Publication date: 14 November 2024

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

zbMATH Keywords

stabilityattractorhyperbolicityweakly hyperbolic invariant setqualitative theory of differential equationsheteroclinic contournontransverse homoclinic point and trajectory

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Dynamics induced by flows and semiflows (37C10) Periodic orbits of vector fields and flows (37C27) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Generic properties, structural stability of dynamical systems (37C20) Attractors of solutions to ordinary differential equations (34D45) Stability theory for smooth dynamical systems (37C75) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

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Review of research on the qualitative theory of differential equations at St. Petersburg University. II: Locally qualitative analysis of essentially nonlinear systems

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