Abstract
We suggest a new approach to the analysis of solutions of complicated conservative (in particular, Hamiltonian) systems, which implies the construction of an approximating extended two-parameter dissipative system of equations whose stable solutions (attractors) are arbitrarily exact approximations to solutions of the original conservative system. On the basis of numerical experiments for several conservative and Hamiltonian systems with two degrees of freedom, we show that, in all these systems, transition to chaos takes place not through the destruction of two-dimensional tori of the unperturbed system but, conversely, through the generation of complicated two-dimensional tori around cycles of the extended dissipative system and through an infinite cascade of bifurcations of the generation of new cycles and singular trajectories in accordance with the Feigenbaum-Sharkovskii-Magnitskii theory.
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