Phase portraits of random planar homogeneous vector fields

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Title:	Phase portraits of random planar homogeneous vector fields
Author:	Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions
Abstract:	Preprint
Abstract:	We study the phase portraits with positive probability of random planar homogeneous vector fields of degree n. In particular, for n=1,2,3, we give a complete solution of the problem and, moreover, either we give the exact value of each probability or we estimate it by using the Monte Carlo method. It is remarkable that all but two of these phase portraits are characterized by their index at the origin and by their number of invariant straight lines through it.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències -Ordinary differential equations -Vector fields -Ordinary differential equations with random coefficients -Planar homogeneous vector fields -Index -Phase portraits -Equacions diferencials ordinàries -Camps vectorials -Classificació AMS::37 Dynamical systems and ergodic theory::37H Random dynamical systems -Classificació AMS::34 Ordinary differential equations::34F05 Equations and systems with randomness
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Document type:	Article - Draft Report
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