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arXiv · 2111.11619

Quasiperiodic Poincare Persistence at High Degeneracy

Weichao Qian·Yong Li·Xue Yang
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Abstract

For Hamiltonian systems with degeneracy of any higher order, we study the persistence of resonant invariant tori, which as some lower-dimensional invariant tori might be elliptic, hyperbolic or of mixed types. Hence we prove a quasiperiodic Poincare theorem at high degeneracy. This answers a long standing conjecture on the persistence of resonant invariant tori in quite general situations.

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Weichao Qian, Yong Li, Xue Yang. 2021-11-23. Quasiperiodic Poincare Persistence at High Degeneracy. https://arxiv.org/abs/2111.11619

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