I know Sprott-A (Nose-Hoover system), and a system Heidel and Zhang investigated in “Nonchaotic and chaotic Behavior in Three-Dimensional Quadratic Systems: Five-One Conservative Cases” (which I think originally was reported by Sprott in 2000). Does anybody know another 3-D chaotic conservative flow?
A lot of examples of chaotic conservative systems are given in my book "Nonlinear Resonance Analysis" (Cambridge University Press, 2010). For instance, a resonance cluster in a 3-wave which consists of two connceted triads (see figure 4.6, p.111 in the book).
Dear Sajad:
There is a chapter titled "Chaos in Conservative Systems" by M. Lakshmanan et al. in their Springer book "Nonlinear Dynamics" (2003). In the introduction of this Chapter, they refer to three systems as examples of conservative chaotic flows:
(1) Henon-Heiles system (1964)
(2) Conservative Duffing Oscillator under periodic forcing
(3) Standard Map (Discrete Chaos)
As system (4), some friends here already mentioned "Sprott-A system" (1994), which is also known as "Nose-Hoover system".
As the Lyapunov exponents are ordered in non-increasing order, for a 3-D conservative chaotic system, we must have L1 + L2 + L3 = 0. As L2 = 0, it follows that L3 = - L1.
My interest is about 4-D conservative chaotic systems. The Lyapunov exponents of such systems have the nice property that L2 = L3 = 0 and L4 = - L1. I am currently working on finding 4-D conservative chaotic systems. (It is not possible for hyperchaos in 4-D conservative chaotic systems).
Regards,
Sundar
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