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arXiv · 2111.10807

A convergence criterion for the unstable manifolds of the MacKay approximate renormalisation

Seul Bee Lee·Stefano Marmi·Tanja I. Schindler
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Abstract

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.

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Seul Bee Lee, Stefano Marmi, Tanja I. Schindler. 2021-11-21. A convergence criterion for the unstable manifolds of the MacKay approximate renormalisation. https://doi.org/10.1016/j.physd.2022.133300

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