Proof of the Morse conjecture for analytic flows on orientable surfaces

Mathematics – Dynamical Systems

Scientific paper

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9 pages

Scientific paper

In 1946, M. Morse proposed a conjecture that an analytic topologically
transitive systems is metrically transitive. We prove this Morse conjecture for
flows on a closed orientable surface of negative Euler characteristic. As a
consequence, the Morse conjecture is true for highly transitive flows on
non-orientable surfaces.

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