Abstract
AbstractLet φ: ℝ × M → M be a continuous flow on a compact C∞ two-manifold M. It is proved that there exists a C1 flow ψ on M which is topologically equivalent to φ, and that the following conditions are equivalent:(a) any minimal set of φ is trivial;(b) φ is topologically equivalent to a C2 flow;(c) φ is topologically equivalent to a C∞ flow.Also proved is a structure and an existence theorem for continuous flows with non-trivial recurrence.
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