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arXiv:2111.10807 [math.DS]AbstractReferencesReviewsResources

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

Seul Bee Lee, Stefano Marmi, Tanja I. Schindler

Published 2021-11-21Version 1

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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