The measure of chaos by the numerical analysis of the fundamental frequencies. Applications to the standard mapping
The first author has developed a new method for the measure of chaos [The chaotic behaviour of the solar system: A numerical estimate of the size of the chaotic zones, Icarus 88, 266-291 (1990)], which is based on the numerical analysis of the variations of fundamental frequencies with time. The method is well suited for the analysis of weakly chaotic motion with many degrees of freedom, and it was first applied for studying the stability of the solar system. As the new method is likely to be of considerable interest for a large range of practical problems, its theoretical foundations with applications to the standard mapping are presented in the paper under review. It is shown that the method allows to obtain an analytical representation of the solution when it is regular, to detect if an orbit is chaotic in a shorter time span as compared with the computation of Lyapunov exponents, and it also gives an estimate of the size of the chaotic zones in the frequency domain.
weakly chaotic motion with many degrees of freedom
scientific article; zbMATH DE number 91656