PreprintarXiv licencearXiv
On the density of Lyapunov unstable elliptic equilibria
Abstract
We prove that any real-analytic Hamiltonian in five or more degrees-of-freedom, with a locally integrable non-degenerate elliptic equilibrium with indefinite quadratic part, can be perturbed within the real analytic category, while preserving the Birkhoff normal form at the equilibrium up to any arbitrary order, so that the equilibrium becomes Lyapunov unstable.
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BibTeX
@misc{fayad2026density,
title = {{On the density of Lyapunov unstable elliptic equilibria}},
author = {Bassam Fayad and Jaime Paradela and Maria Saprykina and Tere M. -Seara},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03722},
eprint = {2609.03722},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03722},
}
RIS
TY - UNPB
TI - On the density of Lyapunov unstable elliptic equilibria
AU - Bassam Fayad
AU - Jaime Paradela
AU - Maria Saprykina
AU - Tere M. -Seara
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03722
UR - https://arxiv.org/abs/2609.03722
AB - We prove that any real-analytic Hamiltonian in five or more degrees-of-freedom, with a locally integrable non-degenerate elliptic equilibrium with indefinite quadratic part, can be perturbed within the real analytic category, while preserving the Birkhoff normal form at the equilibrium up to any arbitrary order, so that the equilibrium becomes Lyapunov unstable.
ER -