Geometry of the phase space of the complex periodic Riccati equation

Title	Geometry of the phase space of the complex periodic Riccati equation
Authors	A. N. Sakharov¹ ¹Nizhny Novgorod State Agricultural Academy
Annotation	Some 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.
Keywords	Rikkati equation, extensions of linear flows, projective flows, rotation number, periodic solutions, M¨obius transformation.
Citation	Sakharov 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: 21.12.2024.