Phase Portraits of Random Planar Homogeneous Vector Fields

被引：3

作者：

Cima, Anna ^{[1
]}

Gasull, Armengol ^{[1
,2
]}

Manosa, Victor ^{[3
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Fac Ciencies, Barcelona 08193, Spain

[2] Ctr Recerca Matemat, Edifici Cc,Campus Bellaterra, Barcelona 08193, Spain

[3] Univ Politecn Cataluna, Dept Matemat, Colom 11, Terrassa 08222, Spain

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2021年 / 20卷 / 01期

关键词：

Ordinary differential equations with random coefficients; Planar homogeneous vector fields; Index; Phase portraits; CLASSIFICATION; INFINITY; POINTS;

D O I：

10.1007/s12346-020-00437-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：27

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