Open AccessNonlinear stability of elliptic equilibria in hamiltonian systems with exponential time estimates
Author(s) -
Daniela Cárcamo-Díaz,
Jesús F. Palacián,
Cláudio Vidal,
Patricia Yanguas
Publication year - 2021
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021073
Subject(s) - hamiltonian system , nonlinear system , mathematics , exponential stability , hamiltonian (control theory) , exponential function , stability (learning theory) , pure mathematics , exponential growth , upper and lower bounds , mathematical analysis , computer science , mathematical optimization , physics , quantum mechanics , machine learning
In the framework of nonlinear stability of elliptic equilibria in Hamiltonian systems with \begin{document}$ n $\end{document} degrees of freedom we provide a criterion to obtain a type of formal stability, called Lie stability. Our result generalises previous approaches, as exponential stability in the sense of Nekhoroshev (excepting a few situations) and other classical results on formal stability of equilibria. In case of Lie stable systems we bound the solutions near the equilibrium over exponentially long times. Some examples are provided to illustrate our main contributions.