THE FINE STRUCTURE OF HAMILTONIAN SYSTEMS REVEALED USING THE FAST LYAPUNOV INDICATOR

摘要

Since the pioneering work of Henon (1964) the search for chaos indicators, especially for Hamiltonian flows, has known several developments. For systems with two degrees of freedom the basic tool is the visual treatment through the Poincare section in which dispersed points are hints of chaos. Although this approach has been successfully extended to systems with three degrees of freedom, i.e. by analyzing points on a four dimensional space through stereoscopic views, slice cuttings (Froeschle 1970,a, Froeschle 1972), etc., it is clear that it becomes almost impossible for systems with more than three degrees of freedom.