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Complexified dynamical systems. (English) Zbl 1120.37050
Summary: 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.

37N99Applications of dynamical systems
37C80Symmetries, equivariant dynamical systems
37C25Fixed points, periodic points, fixed-point index theory