Giraldo Suárez, LuisGascón, Francisco G.2023-06-202023-06-2020001089-765810.1063/1.1286285https://hdl.handle.net/20.500.14352/57586Analysis of the question whether or not a given dynamical system has closed trajectories is of great importance for applications and represents independent theoretical interest. The authors give a new geometrical proof of the extension of the Bendixson-Dulac criterion on the absence of closed trajectories in R3 obtained by V. B. Demidovich [Z. Angew. Math. Mech. 46, 145-146 (1966; Zbl 0138.33303)] and corrected later by K. R. Schneider [Z. Angew. Math. Mech. 49, 441-443 (1969; Zbl 0186.15603)]. Due to the flexibility of the new approach, extensions of the Demidovich criterion to several directions have been obtained. Illustrative examples are considered and some open problems are discussed.engjournal articlehttp://jmp.aip.org/resource/1/JMAPAQ/v41/i9http://www.aip.org/restricted access517.9Demidovich criterionclosed trajectoriesPoincaré-Bendixson theoryDulac criterionEcuaciones diferenciales1202.07 Ecuaciones en Diferencias