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arXiv · 0705.3893

Complexified Dynamical Systems

Carl M. Bender·Darryl D. Holm·Daniel W. Hook
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Abstract

Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an infinitessimal subclass of the full set of complex solutions. This paper examines a subset of the complex solutions that contains the real solutions, namely, those having PT symmetry. The condition of PT symmetry selects out complex solutions that are periodic.

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Carl M. Bender, Darryl D. Holm, Daniel W. Hook. 2007-07-04. Complexified Dynamical Systems. https://doi.org/10.1088/1751-8113/40/32/f02

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