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arXiv · 1501.01670

Transitivity of conservative toral endomorphisms

Martin Andersson
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Abstract

It is shown that if a non-invertible area preserving local homeomorphism on $\mathbb{T}^2$ is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive. This gives a complete characterization, in any smoothness category, of those homotopy classes of conservative endomorphisms that consist entirely of transitive maps.

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Martin Andersson. 2018-06-15. Transitivity of conservative toral endomorphisms. https://doi.org/10.1088/0951-7715%2F29%2F3%2F1047

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