Para depositar en Docta Complutense, identifícate con tu correo @ucm.es en el SSO institucional: Haz clic en el desplegable de INICIO DE SESIÓN situado en la parte superior derecha de la pantalla. Introduce tu correo electrónico y tu contraseña de la UCM y haz clic en el botón MI CUENTA UCM, no autenticación con contraseña.
 

Stability of R 3-dynamical systems with symmetry.

Loading...
Thumbnail Image

Full text at PDC

Publication date

1999

Advisors (or tutors)

Editors

Journal Title

Journal ISSN

Volume Title

Publisher

Società Italiana di Fisica
Citations
Google Scholar

Citation

Abstract

The study of the stability of a periodic solution p of a vector field using either the linear variational equations (associated to the vector field at p ), or the Poincaré map on a cross section, is known to present some difficulties. This work provides some techniques to ascertain the stability of the closed curve C={p 0 (t): t∈R} in the case of an R 3 analytic vector field X → possessing symmetries. It is assumed that one or more symmetry vectors S → are known (the Lie derivative of S → along the streamlines of X → , L X → (S → ) , is zero modulus X → ). One of the cases for which the stability of the closed curve can be determined is that of a divergence-free field X → having a known symmetry S → satisfying L X → (S → )=λ(x)X → and divS → =λ(x) . This is an interesting case because many devices used in the confinement of plasma possess symmetries of this type (X → is the magnetic induction vector B → ) with λ(x)=0 . This type of symmetry implies torus-like magnetic surfaces. It is noted that it constitutes an interesting (and difficult) problem to find examples of vector fields with symmetries for which λ≠0 . All the proofs are simple, and the technique is very nice.

Research Projects

Organizational Units

Journal Issue

Description

UCM subjects

Unesco subjects

Keywords

Collections