A convergence criterion for the unstable manifolds of the MacKay approximate renormalisation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866929281632829440 |
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| author | Lee, Seul Bee Marmi, Stefano Schindler, Tanja I. |
| author_facet | Lee, Seul Bee Marmi, Stefano Schindler, Tanja I. |
| contents | We give an explicit arithmetical condition which guarantees the existence of the unstable manifold of the MacKay approximate renormalisation scheme for the breakup of invariant tori in one and a half degrees of freedom Hamiltonian systems, correcting earlier results. Furthermore, when our condition is violated, we give an example of points on which the unstable manifold does not converge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_10807 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A convergence criterion for the unstable manifolds of the MacKay approximate renormalisation Lee, Seul Bee Marmi, Stefano Schindler, Tanja I. Dynamical Systems 37J40 (Primary) 37F50, 70H08 (Secondary) We give an explicit arithmetical condition which guarantees the existence of the unstable manifold of the MacKay approximate renormalisation scheme for the breakup of invariant tori in one and a half degrees of freedom Hamiltonian systems, correcting earlier results. Furthermore, when our condition is violated, we give an example of points on which the unstable manifold does not converge. |
| title | A convergence criterion for the unstable manifolds of the MacKay approximate renormalisation |
| topic | Dynamical Systems 37J40 (Primary) 37F50, 70H08 (Secondary) |
| url | https://arxiv.org/abs/2111.10807 |