Publicación:
NONLINEAR STABILITY OF EQUILIBRIA IN HAMILTONIAN SYSTEMS WITH MULTIPLE RESONANCES WITHOUT INTERACTIONS

Vista sencilla de ítem
dc.creatorCLAUDIO FERNANDO SIERPE SIERPE
dc.creatorJOSÉ CLAUDIO VIDAL DÍAZ
dc.date2024
dc.date.accessioned2025-01-10T15:51:37Z
dc.date.available2025-01-10T15:51:37Z
dc.date.issued2024
dc.description.abstractIN THIS WORK, WE ADVANCE IN THE STUDY OF THE LYAPUNOV STABILITY AND INSTABILITY OF EQUILIBRIUM SOLUTIONS OF HAMILTONIAN FLOWS. MORE PRECISELY, WE STUDY THE NONLINEAR STABILITY IN THE LYAPUNOV SENSE OF EQUILIBRIUM SOLUTIONS IN AUTONOMOUS HAMILTONIAN SYSTEMS WITH N-DEGREES OF FREEDOM, ASSUMING THE EXISTENCE OF TWO RESONANCE VECTORS K1 AND K2 WITHOUT INTERACTION (|K1|?|K2|). WE PROVIDE CONDITIONS TO OBTAIN A TYPE OF FORMAL STABILITY, CALLED LIE STABILITY. IN PARTICULAR, WE NEED TO NORMALIZE THE HAMIL TONIAN FUNCTION TO ANY ARBITRARY ORDER, AND OUR RESULTS TAKE INTO ACCOUNT THE SIGN OF THE COMPONENTS OF THE RESONANCE VECTORS. SUBSEQUENTLY, WE GUARANTEE SOME SUFFICIENT CONDITIONS TO OBTAIN EXPONENTIAL STABILITY IN THE SENSE OF NEKHOROSHEV FOR LIE STABLE SYSTEMS. IN ADDITION, WE GIVE SUFFICIENT CONDITIONS FOR THE INSTABILITY IN THE LYAPUNOV SENSE OF THE FULL SYSTEM. FOR THIS, IT IS NECESSARY TO NORMALIZE THE HAMILTONIAN FUNCTION TO AN ADEQUATE ORDER, AND ASSUMING THAT THE COMPONENTS OF AT LEAST ONE RESONANCE VECTOR CHANGE OF SIGN.
dc.formatapplication/pdf
dc.identifier.doi10.1007/s44198-024-00192-2
dc.identifier.issn1776-0852
dc.identifier.issn1402-9251
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/13989
dc.languagespa
dc.publisherJOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
dc.relation.uri10.1007/s44198-024-00192-2
dc.rightsPUBLICADA
dc.subjectSatbility
dc.subjectResonance without interaction
dc.subjectNonlinear stability
dc.subjectMultiple resonance
dc.subjectLie normal form
dc.subjectHamiltonian formulation
dc.titleNONLINEAR STABILITY OF EQUILIBRIA IN HAMILTONIAN SYSTEMS WITH MULTIPLE RESONANCES WITHOUT INTERACTIONS
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
ubb.SedeCONCEPCIÓN
Archivos
Colecciones
Artículos científicos