Non-existence of Lyapunov exponents in the Newhouse domain
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915933925146624 |
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| author | Kiriki, Shin Li, Xiaolong Nakano, Yushi Soma, Teruhiko |
| author_facet | Kiriki, Shin Li, Xiaolong Nakano, Yushi Soma, Teruhiko |
| contents | We show that within the Newhouse domain of $C^r$ surface diffeomorphisms ($r \in [2,\infty )$), there exists a dense subset $\mathcal D$ such that for any $f \in \mathcal D$, Lyapunov exponents fail to exist for all points in some open set $U$ and all nonzero tangent vectors in some open cone $V \subset \mathbb{R}^2$. This demonstrates that the non-existence of Lyapunov exponents is a persistent phenomenon in the setting of robust homoclinic tangencies. The proof relies on constructing diffeomorphisms exhibiting specific oscillatory return times near a homoclinic tangency, incorporating techniques from Newhouse theory and recent results on Lyapunov irregularity, alongside several refinements and new arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10913 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-existence of Lyapunov exponents in the Newhouse domain Kiriki, Shin Li, Xiaolong Nakano, Yushi Soma, Teruhiko Dynamical Systems We show that within the Newhouse domain of $C^r$ surface diffeomorphisms ($r \in [2,\infty )$), there exists a dense subset $\mathcal D$ such that for any $f \in \mathcal D$, Lyapunov exponents fail to exist for all points in some open set $U$ and all nonzero tangent vectors in some open cone $V \subset \mathbb{R}^2$. This demonstrates that the non-existence of Lyapunov exponents is a persistent phenomenon in the setting of robust homoclinic tangencies. The proof relies on constructing diffeomorphisms exhibiting specific oscillatory return times near a homoclinic tangency, incorporating techniques from Newhouse theory and recent results on Lyapunov irregularity, alongside several refinements and new arguments. |
| title | Non-existence of Lyapunov exponents in the Newhouse domain |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2604.10913 |