Integral expressions of Lyapunov exponents for autonomous ordinary differential systems

2008 ◽  
Vol 52 (1) ◽  
pp. 195-216 ◽  
Author(s):  
XiongPing Dai
Keyword(s):  
Lyapunov Exponents ◽  
Differential Systems

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.

Codes for Approximating Lyapunov Exponents

2009 ◽  
Author(s):  
Luca Dieci ◽  
Michael S. Jolly ◽  
Erik S. Van Vleck
Keyword(s):  
Lyapunov Exponents ◽  
Jacobian Matrix ◽  
Alternative Strategy ◽  
Differential Systems ◽  
Small Systems ◽  
Large Systems ◽  
Linear Problems ◽  
Qr Methods ◽  
Nonlinear Differential Systems

We present a suite of codes for approximating Lyapunov exponents of nonlinear differential systems by so-called QR methods. The basic solvers perform integration of the trajectory and approximation of the Lyapunov exponents simultaneously. That is, they integrate for the trajectory at the same time, and with the same underlying schemes, as integration for the Lyapunov exponents is carried out. Separate codes solve small systems for which we can compute and store the Jacobian matrix, and for large systems for which the Jacobian matrix cannot be stored, and it may not even be explicitly known. If it is known, the user has the option to provide its action on a vector. An alternative strategy is also presented in which one may want to approximate the trajectory with a specialized solver, linearize around the computed trajectory, and then carry out the approximation of the Lyapunov exponents using codes for linear problems.

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