caa a22 4500 60546104X CHVBK 20210128100241.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10114-015-3663-4 doi (NATIONALLICENCE)springer-10.1007/s10114-015-3663-4 Local phase portraits through the Newton diagram of a vector field [Elektronische Daten] [Antonio Algaba, Isabel Checa, Cristóbal García, Manuel Reyes] The Newton diagram and, in particular, the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine the existence of characteristic orbits and separatrices of an isolated singular point. We give an easy algorithm for obtaining the local phase portrait near the origin of a bi-dimensional differential system and we provide several examples. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Monodromy nationallicence separatrices nationallicence phase portraits nationallicence quasi-homogeneous vector field nationallicence Algaba Antonio Department of Mathematics, Faculty of Experimental Sciences, Avda. Tres de Marzo s/n, 21071, Huelva, Spain aut Checa Isabel Department of Mathematics, Faculty of Experimental Sciences, Avda. Tres de Marzo s/n, 21071, Huelva, Spain aut García Cristóbal Department of Mathematics, Faculty of Experimental Sciences, Avda. Tres de Marzo s/n, 21071, Huelva, Spain aut Reyes Manuel Department of Mathematics, Faculty of Experimental Sciences, Avda. Tres de Marzo s/n, 21071, Huelva, Spain aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/6(2015-06-01), 1015-1034 1439-8516 31:6<1015 2015 31 10114 https://doi.org/10.1007/s10114-015-3663-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-3663-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Algaba Antonio Department of Mathematics, Faculty of Experimental Sciences, Avda. Tres de Marzo s/n, 21071, Huelva, Spain aut NATIONALLICENCE 700 1- Checa Isabel Department of Mathematics, Faculty of Experimental Sciences, Avda. Tres de Marzo s/n, 21071, Huelva, Spain aut NATIONALLICENCE 700 1- García Cristóbal Department of Mathematics, Faculty of Experimental Sciences, Avda. Tres de Marzo s/n, 21071, Huelva, Spain aut NATIONALLICENCE 700 1- Reyes Manuel Department of Mathematics, Faculty of Experimental Sciences, Avda. Tres de Marzo s/n, 21071, Huelva, Spain aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/6(2015-06-01), 1015-1034 1439-8516 31:6<1015 2015 31 10114