Hilbert's 16th problem: Limit cycles of polynomial vector fields in the plane

1975 ◽  
pp. 55-57
Author(s):  
Charles Pugh
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Hilbert’S 16Th Problem ◽  
Hilbert's 16Th Problem

Limit cycles of three-dimensional polynomial vector fields

Nonlinearity ◽  
2004 ◽  
Vol 18 (1) ◽  
pp. 175-209 ◽  
Author(s):  
Marcin Bobie ski ◽  
Henryk o a dek
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Three Dimensional ◽  
Polynomial Vector ◽  
Polynomial Vector Fields

BIFURCATIONS OF LIMIT CYCLES IN A Z2-EQUIVARIANT PLANAR POLYNOMIAL VECTOR FIELD OF DEGREE 7

2006 ◽  
Vol 16 (04) ◽  
pp. 925-943 ◽  
Author(s):  
JIBIN LI ◽  
MINGJI ZHANG ◽  
SHUMIN LI
Keyword(s):  
Vector Field ◽  
Dynamical Systems ◽  
Limit Cycles ◽  
Bifurcation Theory ◽  
Vector Fields ◽  
Compound Eyes ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Planar Dynamical Systems ◽  
Equivariant Vector Field

By using the bifurcation theory of planar dynamical systems and the method of detection functions, the bifurcations of limit cycles in a Z2-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 7 are studied. An example of a special Z2-equivariant vector field having 50 limit cycles with a configuration of compound eyes are given.

scholarly journals Limit cycles of planar polynomial vector fields

Scholarpedia ◽  
2010 ◽  
Vol 5 (8) ◽  
pp. 9648 ◽  
Author(s):  
Maoan Han ◽  
Jibin Li ◽  
Chengzhi Li
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Polynomial Vector ◽  
Polynomial Vector Fields
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