Measures of Chaos in Hamiltonian Systems

Abstract

Hamiltonian systems with two or more degrees of freedom are generally nonintegrable which usually involves chaotic dynamics. The size of the chaotic sets determines for a large part the nature and influence of chaos. Near stable equilibrium we can obtain normal forms that often produce ‘formal integrability’ of the Hamiltonian system and at the same time produce rigorous but not necessarily optimal upper limits for the size, the measure of chaotic sets. This is demonstrated for two and three degrees of freedom systems with attention to the role of symmetry.