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Geometry of the phase space of the complex periodic Riccati equation

TitleGeometry of the phase space of the complex periodic Riccati equation
AuthorsA. N. Sakharov1
1Nizhny Novgorod State Agricultural Academy
AnnotationSome questions related to the problem of describing topologies of trajectories of complex Riccati equations with periodic coefficients are considering. Such an equation is the result of prektivization of a linear system of differential equations with periodic coefficients. It is clear that the behavior of a linear periodic system is completely described by the theorem Floquet-Lyapunov. In a two-dimensional case, however, one can define and the complete topological invariant of the flow generated by this system. In the complex case, a number of well-known results are refined.
KeywordsRikkati equation, extensions of linear flows, projective flows, rotation number, periodic solutions, M¨obius transformation.
CitationSakharov A. N. ''Geometry of the phase space of the complex periodic Riccati equation'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 14-18, 2022). Saransk: SVMO Publ, 2022. - pp. 178-184. Available at: https://conf.svmo.ru/files/2022/papers/paper28.pdf. - Date of access: 30.11.2022.