scholarly journals Nonlinear perturbations of evolution systems in scales of Banach spaces

Nonlinearity ◽  
2020 ◽  
Vol 33 (11) ◽  
pp. 6134-6156
Author(s):  
Martin Friesen ◽  
Oleksandr Kutoviy
Keyword(s):  
Banach Spaces ◽  
Nonlinear Perturbations ◽  
Scales Of Banach Spaces ◽  
Evolution Systems

Conjugacies between linear and nonlinear non-uniform contractions

2008 ◽  
Vol 28 (1) ◽  
pp. 1-19 ◽  
Author(s):  
LUIS BARREIRA ◽  
CLAUDIA VALLS
Keyword(s):  
Banach Spaces ◽  
Discrete Time ◽  
Linear Operators ◽  
Nonlinear Perturbations ◽  
Exponential Dichotomies ◽  
Locally Lipschitz ◽  
Linear And Nonlinear

AbstractWe construct conjugacies between linear and nonlinear non-uniform exponential contractions with discrete time. We also consider the general case of a non-autonomous dynamics defined by a sequence of maps. The results are obtained by considering both linear and nonlinear perturbations of the dynamics xm+1=Amxm defined by a sequence of linear operators Am. In the case of conjugacies between linear contractions we describe them explicitly. All the conjugacies are locally Hölder, and in fact are locally Lipschitz outside the origin. We also construct conjugacies between linear and nonlinear non-uniform exponential dichotomies, building on the arguments for contractions. All the results are obtained in Banach spaces.

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