Closed poly-trajectories and Poincaré index of non-smooth vector fields on the plane

被引：0
作者：
C. A. Buzzi
T. de Carvalho
P. R. da Silva
机构：
[1] UNESP - Univ Estadual Paulista,
[2] UNESP - Univ Estadual Paulista,undefined
来源：
Journal of Dynamical and Control Systems | 2013年 / 19卷
关键词：
Limit cycles; vector fields; singular perturbation; non-smooth vector fields; heteroclinic orbits; Poincaré index; closed poly-trajectory; 34C20; 34C26; 34D15; 34H05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a class of non-smooth vector fields we provide necessary and sufficient conditions for the existence of closed poly-trajectorie. By means of a regularization process we prove that hyperbolic closed poly-trajectories are limit sets of a sequence of limit cycles of smooth vector fields. In our approach the Poincaré Index for non-smooth vector fields is introduced.
引用
收藏
页码：173 / 193
页数：20
相关论文
共 17 条
[1]  
Buzzi CA(2005)Singular perturbation problems for time reversible systems Proc. Amer. Math. Soc. 133 3323-3331
[2]  
da Silva PR(2006)A singular approach to discontinuous vector fields on the plane J. Differential Equations 231 633-655
[3]  
Teixeira MA(1979)Geometric singular perturbation theory for ordinary differential equations J. Differential Equations 31 53-98
[4]  
Buzzi CA(1984)Roughness of a discontinuous system Vestinik Moskovskogo Universiteta, Matematika 5 16-20
[5]  
da Silva PR(2008)Sliding vector fields via slow-fast systems Bull. Belg. Math. Soc. Simon Stevin 15–5 851-869
[6]  
Teixeira MA(2002)Structurally stable discontinuous vector fields on the plane Qual. Theory of Dynamical Systems 3 227-250
[7]  
Fenichel N(2001)Impasse singularities of differential systems of the form J. Differential Equations 169 567-587
[8]  
Kozlova VS(1991)( J. Differential Equations 92 252-281
[9]  
Llibre J(1991)) An. Acad. Brasil Cienc. 53 257-260
[10]  
Silva PR(undefined)′ = undefined undefined undefined-undefined
12