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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.

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