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arXiv 2011.109972020-11math.DS

On the rigidity of integrable deformations of twist maps and Hamiltonian flows

Jessica Elisa Massetti, Alfonso Sorrentino

备注：: It has been replaced by arXiv:2202.00313

英文摘要：

In this article we investigate rigidity properties of integrable area-preserving twist maps of the cylinder. More specifically, we prove that if a deformation of the standard integrable map preserves rotational invariant circles (i.e., homotopically non-trivial invariant curves of the cylinder on which the dynamics is conjugate to a rotation) for any rational rotation number in an open interval (without any further assumption on its size), then the deformation must be trivial. Analogue phenomena for integrable Tonelli Hamiltonian flows in higher dimensions are discussed.

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