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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Lyapunov unstable elliptic equilibria
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by Bassam Fayad
J. Amer. Math. Soc. 36 (2023), 81-106
DOI: https://doi.org/10.1090/jams/997
Published electronically: January 27, 2022

Abstract:

A new diffusion mechanism from the neighborhood of elliptic equilibria for Hamiltonian flows in three or more degrees of freedom is introduced. We thus obtain explicit real entire Hamiltonians on $\mathbb {R}^{2d}$, $d\geq 4$, that have a Lyapunov unstable elliptic equilibrium with an arbitrary chosen frequency vector whose coordinates are not all of the same sign. For non-resonant frequency vectors, our examples all have divergent Birkhoff normal form at the equilibrium.

On $\mathbb {R}^4$, we give explicit examples of real entire Hamiltonians having an equilibrium with an arbitrary chosen non-resonant frequency vector and a divergent Birkhoff normal form.

References
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Bibliographic Information
  • Bassam Fayad
  • Affiliation: Institut de Mathématiques de Jussieu–Paris Rive Gauche (IMJ-PRG), French National Centre for Scientific Research (CNRS), 58-56, Avenue de France, Paris, France
  • MR Author ID: 675142
  • Received by editor(s): July 2, 2020
  • Received by editor(s) in revised form: May 20, 2021, September 1, 2021, and October 18, 2021
  • Published electronically: January 27, 2022
  • © Copyright 2022 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 36 (2023), 81-106
  • MSC (2020): Primary 37J06, 37J11, 37J12, 37J25, 37J30
  • DOI: https://doi.org/10.1090/jams/997
  • MathSciNet review: 4495839