Simple Conservative, Autonomous, Second-Order Chaotic Complex Variable Systems

Delmar Marshall
Physics Department, Amrita Vishwa Vidyepeetham, Clappana P.O., Kollam, Kerala 690-525, India

J. C. Sprott
Physics Department, University of Wisconsin, 1150 University Avenue, Madison, WI 53706, USA

(Received April 22, 2008; Revised July 21, 2009)

ABSTRACT

It is shown that, for analytic functiions f, systems of the form z'' = f(z, z') and z'' = f(z) cannot produce chaos, and that systems of the form z'' = f(z, z*) are conservative. Eight simple chaotic systems of the form z'' = f(z, z*) with quadratic and cubic polynomial f(z, z*) are given. Lyapunov spectra are calculated, and the systems' phase space trajectories are displayed. For each system, a Hamiltonian is given, if one exists.

Ref: D. Marshall and J. C. Sprott, Chaos 20, 697-702 (2010)

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