The power of chaos

Numerical experiments performed with the Hénon-Heiles oscillator reveal that quasi-periodic and chaotic solutions of Hamiltonian systems can be differentiated on the basis of the structure of their power spectra. While we illustrate in this paper that mere visual inspection of the distribution of power already discloses striking differences between both classes of solution, we attempt to develop more objective structural criteria.It is found that the fractal dimension of the renormalised power spectrum lends itself to a convenient global characterisation of the geometry of the latter, capable, in principle, of discriminating between quasi-periodicity and chaos.