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Stably ergodic endomorphisms with positive Lyapunov exponents
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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BibTeX
@misc{andersson2026stably,
title = {{Stably ergodic endomorphisms with positive Lyapunov exponents}},
author = {Martin Andersson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17000},
eprint = {2610.17000},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17000},
}
RIS
TY - UNPB
TI - Stably ergodic endomorphisms with positive Lyapunov exponents
AU - Martin Andersson
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17000
UR - https://arxiv.org/abs/2610.17000
AB - 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.
ER -