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arXiv · 2610.17000

Stably ergodic endomorphisms with positive Lyapunov exponents

Martin Andersson
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Abstract

We introduce a new criterion which guarantees that a conservative local diffeomorphism is both non-uniformly expanding (in particular has all its Lyapunov exponents positive) and stably ergodic. The criterion involves averaging expansion rates over preimages and allows us to construct explicit examples in a variety of homotopy classes, including those represented by linear endomorphisms with contracting directions.

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Martin Andersson. 2026-10-12. Stably ergodic endomorphisms with positive Lyapunov exponents. https://arxiv.org/abs/2610.17000

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