Abstract

The standard map is an apparently simple system that is well suited to explain the transition from regular behaviour to global chaos. Its dynamics depends strongly on a control parameter that influences the degree of chaos. For low or high parameter values the resulting dynamics is entirely regular or chaotic. At intermediate parameter values, however, the map exhibits a complex behaviour characterized by a mixture of chaotic and regular regions in the phase space. It is the purpose of this paper to emphasize this remarkable dynamics. Using phase planes and the Orthogonal Fast Lyapunov Indicator (OFLI) plots we try to determine the control parameter levels at which the main transformations take place and determine how quickly the chaotic orbits replace the regular ones in the phase space. Some comments referring the implementation and the efficiency of the OFLI test are included in the paper.