Nonlinear stability of elliptic equilibria in Hamiltonian systems with exponential time estimates
Fecha
2021Autor
Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Impacto
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10.3934/dcds.2021073
Resumen
In the framework of nonlinear stability of elliptic equilibria in Hamiltonian systems with n 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 ...
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In the framework of nonlinear stability of elliptic equilibria in Hamiltonian systems with n 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. [--]
Materias
Elliptic equilibria,
Resonances,
Formal stability,
Lie stability,
Exponential time estimates
Editor
American Institute of Mathematical Sciences (AIMS)
Publicado en
Discrete and Continuous Dynamical Systems, 2021, 41 (11): 5183-5208
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
Versión del editor
Entidades Financiadoras
The authors are partially supported by Projects MTM 2014-59433-C2-1-P of the Ministry of
Economy and Competitiveness of Spain and MTM 2017-88137-C2-1-P of the Ministry of Science,
Innovation and Universities of Spain. D. C.-D. acknowledges support from CONICYT PhD/2016-
21161143. C. Vidal is partially supported by Fondecyt, grant 1180288.