scholarly journals On the linearization theorem for nonautonomous differential equations

2015 ◽  
Vol 139 (7) ◽  
pp. 829-846 ◽  
Author(s):  
Yong-Hui Xia ◽  
Rongting Wang ◽  
Kit Ian Kou ◽  
Donal O'Regan
Keyword(s):  
Differential Equations ◽  
Linearization Theorem ◽  
Nonautonomous Differential Equations

scholarly journals The Bohl Spectrum for Linear Nonautonomous Differential Equations

2016 ◽  
Vol 29 (4) ◽  
pp. 1459-1485 ◽  
Author(s):  
Thai Son Doan ◽  
Kenneth J. Palmer ◽  
Martin Rasmussen
Keyword(s):  
Differential Equations ◽  
Nonautonomous Differential Equations

scholarly journals MORSE SPECTRUM FOR NONAUTONOMOUS DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 08 (03) ◽  
pp. 351-363 ◽  
Author(s):  
FRITZ COLONIUS ◽  
PETER E. KLOEDEN ◽  
MARTIN RASMUSSEN
Keyword(s):  
Differential Equations ◽  
Finite Time ◽  
Accumulation Point ◽  
Morse Decomposition ◽  
Finite Time Lyapunov Exponents ◽  
The Past ◽  
Accumulation Points ◽  
Morse Spectrum ◽  
Nonautonomous Differential Equations ◽  
Linear Cocycle

The concept of a Morse decomposition consisting of nonautonomous sets is reviewed for linear cocycle mappings w.r.t. the past, future and all-time convergences. In each case, the set of accumulation points of the finite-time Lyapunov exponents corresponding to points in a nonautonomous set is shown to be an interval. For a finest Morse decomposition, the Morse spectrum is defined as the union of all of the above accumulation point intervals over the different nonautonomous sets in such a finest Morse decomposition. In addition, Morse spectrum is shown to be independent of which finest Morse decomposition is used, when more than one exists.

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