Title | Geometry of the phase space of the complex periodic Riccati equation |
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Authors | A. N. Sakharov^{1}^{1}Nizhny 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: 29.05.2024. |

**© SVMO, National Research Mordovia State University, 2024**

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