scholarly journals Invariant Manifolds for Abstract Functional Differential Equations and Related Volterra Difference Equations in a Banach Space

2007 ◽  
Vol 50 (1) ◽  
pp. 133-170 ◽  
Author(s):  
Satoru Murakami ◽  
Yutaka Nagabuchi
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Difference Equations ◽  
Invariant Manifolds ◽  
Functional Differential Equations ◽  
Functional Differential ◽  
Volterra Difference Equations

Flows on centre manifolds for scalar functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 193-201 ◽  
Author(s):  
Jack K. Hale
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Imaginary Axis ◽  
Functional Differential Equations ◽  
Zero Eigenvalue ◽  
Functional Differential ◽  
Centre Manifolds ◽  
Scalar Functional ◽  
Linear Scalar

SynopsisBy assuming that a linear scalar functional differential equation (FDE) has only the zero eigenvalue on the imaginary axis, it is shown that the flows on the centre manifolds of all Cr-perturbations of this equation coincide with the flows obtained from scalar ordinary differential equations (ODEs) of order m, where m is the multiplicity of the zero eigenvalue. Furthermore, it is shown that the above situation can be realized through differential difference equations with m – 1 fixed distinct delays.

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