Homoclinic tangency of codimension 2 and historic wandering domains
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917275786805248 |
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| author | Yamamoto, Kodai |
| author_facet | Yamamoto, Kodai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14535 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homoclinic tangency of codimension 2 and historic wandering domains Yamamoto, Kodai Dynamical Systems 37C20, 37C29, 37C70 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. |
| title | Homoclinic tangency of codimension 2 and historic wandering domains |
| topic | Dynamical Systems 37C20, 37C29, 37C70 |
| url | https://arxiv.org/abs/2602.14535 |