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- Title
Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations.
- Authors
Kuznetsov, N.; Alexeeva, T.; Leonov, G.
- Abstract
Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions ( Lyapunov characteristic exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system ( Lyapunov exponents, LEs). In this work, the relation between Lyapunov exponents and Lyapunov characteristic exponents is discussed. The invariance of Lyapunov exponents for regular and irregular linearizations under the change of coordinates is demonstrated.
- Subjects
LYAPUNOV exponents; DIMENSIONS; LINEAR systems; ISOMORPHISM (Crystallography); MATHEMATICAL symmetry
- Publication
Nonlinear Dynamics, 2016, Vol 85, Issue 1, p195
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-016-2678-4