arXiv
Open Access
2018
Lyapunov unstable elliptic equilibria
Bassam Fayad
Abstrak
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 $\R^{2d}$, $d\geq 4$, 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 $\R^4$, 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.
Topik & Kata Kunci
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Bassam Fayad
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2018
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓