Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations
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.
Keywords
Cite
@article{arxiv.1410.2016,
title = {Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations},
author = {N. V. Kuznetsov and T. A. Alexeeva and G. A. Leonov},
journal= {arXiv preprint arXiv:1410.2016},
year = {2016}
}
Comments
Keywords: chaos, Lyapunov exponent, Lyapunov characteristic exponent, Lyapunov dimension of attractor, time-varying linearization, regular and non regular linearization, time reparametrization, change of coordinates, Perron effect of Lyapunov exponent sign reversal