Artículo
The Lyapunov exponents and the neighbourhood of periodic orbits
Fecha de publicación:
05/2020
Editorial:
Wiley Blackwell Publishing, Inc
Revista:
Monthly Notices of the Royal Astronomical Society
ISSN:
0035-8711
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We show that the Lyapunov exponents of a periodic orbit can be easily obtained from the eigenvalues of the monodromy matrix. It turns out that the Lyapunov exponents of simply stable periodic orbits are all zero, simply unstable periodic orbits have only one positive Lyapunov exponent, doubly unstable periodic orbits have two different positive Lyapunov exponents and the two positive Lyapunov exponents of complex unstable periodic orbits are equal. We present a numerical example for periodic orbits in a realistic galactic potential. Moreover, the center manifold theorem allowed us to show that stable, simply unstable and doubly unstable periodic orbits are the mothers of families of, respectively, regular, partially and fully chaotic orbits in their neighbourhood.
Palabras clave:
CHAOS
,
INSTABILITIES
,
GALAXIES: KINEMATICS AND DYNAMICS
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(IALP)
Articulos de INST.DE ASTROFISICA LA PLATA
Articulos de INST.DE ASTROFISICA LA PLATA
Citación
Carpintero, Daniel Diego; Muzzio, Juan Carlos; The Lyapunov exponents and the neighbourhood of periodic orbits; Wiley Blackwell Publishing, Inc; Monthly Notices of the Royal Astronomical Society; 495; 2; 5-2020; 1608-1612
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