Carregant...
Fitxers
Tipus de document
ArticleVersió
Versió acceptadaData de publicació
Tots els drets reservats
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/193842
Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones
Títol de la revista
Autors
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
The purpose of this paper is to study phenomena in chaotic zones of area preserving maps using simpler models which are easier to analyse theoretically and numerically. First of all the study of the dynamics in a neighbourhood of the separatrices of a resonant zone is carried out. The well-known separatrix map, defined on a figure eight when needed, is used to determine the location of rotational invariant curves (r.i.c.) inside and outside the resonance. The interest in this part is on a quantitative description of the dynamics in a neighbourhood of the separatrices: to produce theoretical estimates of the width of the stochastic zone, distance to the r.i.c., existence of tiny islands close to the separatrices, . . . In every one of the studied items one has tried to complement the limit analytic study with realistic numerical simulations, describing the analogy when possible. After this study, we focus on the formation of larger domains without r.i.c. (e.g. Birkhoff domains). To this end we introduce the biseparatrix map model. Although this is a qualitative model, the mechanism of destruction of the "last" r.i.c., and hence the process of creation of zones without r.i.c., is clarified by means of this simple model. Several numerical examples illustrate the results obtained and are used as a test of the theoretical quantitative predictions.
Matèries (anglès)
Citació
Citació
SIMÓ, Carles, VIEIRO YANES, Arturo. Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones. _Physica D_. 2011. Vol. 240, núm. 8, pàgs. 732-753. [consulta: 24 de gener de 2026]. ISSN: 0167-2789. [Disponible a: https://hdl.handle.net/2445/193842]