The energy function for gradient-like diffeomorphisms on 3-manifolds
In 1978 Conley proved the existence of a continuous Lyapunov function for any flow on a smooth closed manifold and it is now regarded as the fundamental theorem of the dynamical systems. It is also known that for any Morse-Smale diffeomorphism the chain recurrent set coincides with the set of periodic orbits. The authors obtain existence conditions for self-indexing energy functions.
scientific article; zbMATH DE number 5656080
scientific article