Phase portraits of random planar homogeneous vector fields
Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtiques)

Date:	2021
Abstract:	In this paper, we study the probability of occurrence of phase portraits in the set of random planar homogeneous polynomial vector fields, of degree n. In particular, for n= 1, 2, 3, we give the complete solution of the problem; that is, we either give the exact value of each probability of occurrence or we estimate it by using the Monte Carlo method. Remarkably is that all but two of these phase portraits are characterized by the index at the origin and by the number of invariant straight lines through this point.
Grants:	Ministerio de Ciencia e Innovación PID2019-104658GB-I00 Ministerio de Ciencia e Innovación DPI2016-77407-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-388
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Ordinary differential equations with random coefficients ; Planar homogeneous vector fields ; Index ; Phase portraits
Published in:	Qualitative theory of dynamical systems, Vol. 20, Issue 1 (April 2021) , art. 3, ISSN 1662-3592

DOI: 10.1007/s12346-020-00437-7

Postprint 30 p, 504.7 KB

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