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Proof of the Morse conjecture for analytic flows on orientable surfaces

S. Aranson·E. Zhuzhoma
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Abstract

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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S. Aranson, E. Zhuzhoma. 2004-12-05. Proof of the Morse conjecture for analytic flows on orientable surfaces. https://arxiv.org/abs/math/0412098

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