Abstract
Abstract This paper describes a simple three-dimensional time-reversible system of ODEs with quadratic nonlinearities and the unusual property that it is exhibits conservative behavior for some initial conditions and dissipative behavior for others. The conservative regime has quasi-periodic orbits whose amplitude depend on the initial conditions, while the dissipative regime is chaotic. Thus a strange attractor coexists with an infinite set of nested invariant tori in the state space.
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