Normal forms for almost periodic differential systems

2009 ◽  
Vol 29 (2) ◽  
pp. 637-656 ◽  
Author(s):  
WEIGU LI ◽  
JAUME LLIBRE ◽  
HAO WU
Keyword(s):  
Lyapunov Exponents ◽  
Normal Forms ◽  
Almost Periodic ◽  
Differential Systems

AbstractIn this paper we prove smooth conjugate theorems of Sternberg type for almost periodic differential systems, based on the Lyapunov exponents of the corresponding reduced systems.

scholarly journals (ω, c)- Pseudo almost periodic distributions

2020 ◽  
Vol 7 (1) ◽  
pp. 237-248 ◽  
Author(s):  
Mohammed Taha Khalladi ◽  
Abdelkader Rahmani
Keyword(s):  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Differential Systems ◽  
Schwartz Distributions ◽  
Pseudo Almost Periodic Solutions ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
Pseudo Almost Periodicity ◽  
Pseudo Almost Periodic

AbstractThe paper is a study of the (w, c) −pseudo almost periodicity in the setting of Sobolev-Schwartz distributions. We introduce the space of (w, c) −pseudo almost periodic distributions and give their principal properties. Some results about the existence of distributional (w, c) −pseudo almost periodic solutions of linear differential systems are proposed.

Frameworks Application for Estimation of Lyapunov Exponents for Systems with Periodic Coeffi cients

2020 ◽  
Vol 21 (1) ◽  
pp. 3-13
Author(s):  
N. N. Karabutov
Keyword(s):  
Lyapunov Exponents ◽  
Identification Problem ◽  
Almost Periodic ◽  
Histogram Method ◽  
Index Set ◽  
Periodic Coefficients ◽  
Order Estimation ◽  
Coeffi Cients ◽  
Problem Solve ◽  
System Order

The identification problem of Lyapunov exponents is considered for dynamic systems with periodic coefficients under uncertainty. Indexes identification is based on the analysis of a special class of frameworks describing dynamics of indexes change. The method of frameworks obtaining is described. The adequacy concept of obtained estimations Lyapunov exponents is introduced. The adequacy criterion is based on the analysis of the structure definition domain. The domain which belongs to the set of Lyapunov exponents estimates is determined. The method proposed for the order estimation of the system. The method is based on the properties analysis of almost periodic to Bohr functions and proposed frameworks. The case when lineals for Lyapunov exponents are crossed is considered. WE obtain to an infinite spectrum of Lyapunov exponents. Upper bound for the smallest index and mobility limit for the large index are obtained and the index set of the system is determined. The graphics criteria based on the analysis of framework properties are proposed for the adequacy estimation of obtained indexes. The histogram method is applied to check of estimations set. It is shown that a dynamic system with periodic coefficients can have a set of Lyapunov exponents. The extension of almost periodic functions on Bohr is proposed to the problem solve of Lyapunov exponents evaluation. The system order estimation is obtained on the basis of the framework property analysis.

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