Existence of an energy function for three-dimensional chaotic sink-source cascades

This paper is a continuation of research in the direction of energy function (a smooth Lyapunov function whose set of critical points coincides with the chain recurrent set of a system) construction for discrete dynamical systems. The authors established the existence of an energy function for any A-diffeomorphism of a three-dimensional closed orientable manifold whose non-wandering set consists of a chaotic one-dimensional canonically embedded surface attractor and repeller. Published under an exclusive license by AIP Publishing.

Automated summary

This paper continues research on constructing energy functions for discrete dynamical systems, with a focus on A-diffeomorphisms of three-dimensional closed orientable manifolds. The authors demonstrate the existence of an energy function where the non-wandering set includes a chaotic one-dimensional canonically embedded surface attractor and repeller.