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We prove the existence of a continuous Morse energy function for an arbitrarytopological flow with finite hyperbolic (in topological sense) chain recurrentset on a topological manifold of any dimension. This result is a partialsolution of the Morse problem of existence of continuous Morse functions on anytopological manifolds. Namely, we prove that a topological manifold admits acontinuous Morse function if it admits a topological flow with finitehyperbolic chain recurrent set.

On existence of a Morse energy function for topological flows with finite chain recurrent sets