The relative Lyapunov indicator: an efficient method of chaos detection
In recent years there has been a growing interest in the development and application of different chaos detection methods. Besides the traditional tools, i.e. maximum Lyapunov characteristic exponent, frequency analysis etc. several new methods have been developed, which can be used to detect ordered and chaotic nature of individual orbits, or to separate regions of ordered and chaotic motions in the phase space of a dynamical system. One of these methods is the fast Lyapunov indicator (FLI) method. The time evolution of the FLI indicates clearly the ordered or chaotic nature of an orbit. Here, a new chaos detection method called the relative Lyapunov indicator (RLI) is introduced. The definition of the RLI is complex enough and connected with the Lyapunov characteristic exponent (LCE) and its finite-time approximation called the finite-time Lyapunov indicator (LI). An application of the RLI method to symplectic mappings and to a continuous Hamiltonian system (the restricted four-body problem related with the exo-planetary system) is considered.
scientific article; zbMATH DE number 2140272