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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.00499 |
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| _version_ | 1866915221438726144 |
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| author | Kajihara, Yuika Motonaga, Shoya Shinoda, Mao |
| author_facet | Kajihara, Yuika Motonaga, Shoya Shinoda, Mao |
| contents | We consider the Aubry set for the XY model, symbolic dynamics $([0,1]^{\mathbb{N}_0},σ)$ with the uncountable symbol $[0,1]$, and study its action-optimizing properties. Moreover, for a potential function that depends on the first two coordinates we obtain an explicit expression of the set of optimal periodic measures and a detailed description of the Aubry set. We also show the typicality of periodic optimization for 2-locally constant potentials with the twist condition. Our approach combines the weak KAM method for symbolic dynamics and variational techniques for twist maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Aubry set for the XY model and typicality of periodic optimization for 2-locally constant potentials Kajihara, Yuika Motonaga, Shoya Shinoda, Mao Dynamical Systems We consider the Aubry set for the XY model, symbolic dynamics $([0,1]^{\mathbb{N}_0},σ)$ with the uncountable symbol $[0,1]$, and study its action-optimizing properties. Moreover, for a potential function that depends on the first two coordinates we obtain an explicit expression of the set of optimal periodic measures and a detailed description of the Aubry set. We also show the typicality of periodic optimization for 2-locally constant potentials with the twist condition. Our approach combines the weak KAM method for symbolic dynamics and variational techniques for twist maps. |
| title | The Aubry set for the XY model and typicality of periodic optimization for 2-locally constant potentials |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.00499 |