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arXiv · 2602.14535

Homoclinic tangency of codimension 2 and historic wandering domains

Kodai Yamamoto
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Abstract

We construct a four-dimensional diffeomorphism exhibiting a homoclinic tangency of the largest codimension, which admits a historic wandering domain of positive Lebesgue measure. Every orbit in this wandering domain exhibits historic behavior, in the sense that time averages do not converge. This example shows that homoclinic tangencies of the largest codimension can still give rise to positive Lebesgue measure sets with non-convergent statistical behavior.

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Kodai Yamamoto. 2026-02-16. Homoclinic tangency of codimension 2 and historic wandering domains. https://arxiv.org/abs/2602.14535

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