Abstract
A new approach to the analysis of solutions of complex conservative and, in particular, Hamiltonian systems is proposed, which involves construction of an approximating augmented two-parameter dissipative system of equations whose stable solutions (attractors) are arbitrarily accurate approximations to the solutions of the original conservative system. Numerical calculations for several four-dimensional conservative systems and for Hamiltonian systems with two or three degrees of freedom show that in all these systems the transition to chaos does not occur via breakup of two-dimensional or three-dimensional unperturbed-system toruses, but conversely via the birth of complex two-dimensional toruses around the cycles of the augmented dissipative system and via an infinite bifurcation cascade creating new cycles and singular trajectories in accordance with the Feigenbaum‐Sharkovskii‐Magnitskii theory. We thus lay a foundation for the development of a unified universal theory of dynamical chaos in nonlinear systems of differential equations of all types.
Published Version
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