PreprintCC BY 4.0arXiv
Nonintegrability theorem on perturbed integrable Hamiltonian dynamical systems with two independent resonances
Abstract
In this paper we establish a new theorem for nonintegrability of a perturbed, autonomous, two-degree-of-freedom Hamiltonian dynamical system with two independent resonances, based on a criterion which utilizes the well-known theorem of Poincaré and a Lie-series symplectic transformation. We also make certain assumptions and suggestions as to when the theorem holds and when it does not.
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BibTeX
@misc{zafeiriadis2026nonintegrability,
title = {{Nonintegrability theorem on perturbed integrable Hamiltonian dynamical systems with two independent resonances}},
author = {Nikos Zafeiriadis and Efthymia Meletlidou and Christos Efthymiopoulos and Christos Volos},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04962},
eprint = {2611.04962},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04962},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonintegrability theorem on perturbed integrable Hamiltonian dynamical systems with two independent resonances
AU - Nikos Zafeiriadis
AU - Efthymia Meletlidou
AU - Christos Efthymiopoulos
AU - Christos Volos
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04962
UR - https://arxiv.org/abs/2611.04962
AB - In this paper we establish a new theorem for nonintegrability of a perturbed, autonomous, two-degree-of-freedom Hamiltonian dynamical system with two independent resonances, based on a criterion which utilizes the well-known theorem of Poincaré and a Lie-series symplectic transformation. We also make certain assumptions and suggestions as to when the theorem holds and when it does not.
ER -