2026-06-27T10:18:16Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/575862023-08-25T12:41:16Zcom_20.500.14352_14col_20.500.14352_15

Giraldo Suárez, Luis Gascón, Francisco G. 2023-06-20T16:59:35Z 2023-06-20T16:59:35Z 2000 1089-7658 10.1063/1.1286285 https://hdl.handle.net/20.500.14352/57586 http://jmp.aip.org/resource/1/JMAPAQ/v41/i9 http://www.aip.org/ Analysis 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. eng restricted access New proof and generalizations of the Demidowitsch-Schneider criterion journal article