The Lyapunov exponents and the neighbourhood of periodic orbits

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 unstab...

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Autores principales: Carpintero, Daniel Diego, Muzzio, Juan Carlos
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2020
Materias:
Ciencias Astronómicas
Astronomía
chaos
instabilities
galaxies: kinematics and dynamics
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/125462
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-125462
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Astronómicas
Astronomía
chaos
instabilities
galaxies: kinematics and dynamics
spellingShingle Ciencias Astronómicas
Astronomía
chaos
instabilities
galaxies: kinematics and dynamics
Carpintero, Daniel Diego
Muzzio, Juan Carlos
The Lyapunov exponents and the neighbourhood of periodic orbits
topic_facet Ciencias Astronómicas
Astronomía
chaos
instabilities
galaxies: kinematics and dynamics
description 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.
format Articulo
Preprint
author Carpintero, Daniel Diego
Muzzio, Juan Carlos
author_facet Carpintero, Daniel Diego
Muzzio, Juan Carlos
author_sort Carpintero, Daniel Diego
title The Lyapunov exponents and the neighbourhood of periodic orbits
title_short The Lyapunov exponents and the neighbourhood of periodic orbits
title_full The Lyapunov exponents and the neighbourhood of periodic orbits
title_fullStr The Lyapunov exponents and the neighbourhood of periodic orbits
title_full_unstemmed The Lyapunov exponents and the neighbourhood of periodic orbits
title_sort lyapunov exponents and the neighbourhood of periodic orbits
publishDate 2020
url http://sedici.unlp.edu.ar/handle/10915/125462
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