Stability of parabolic points of area preserving analytic diffeomorphisms

• Simó , Carles ^[1]
  1. [1] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Nº 22, 1980, págs. 67-70
• Idioma: inglés
• DOI: 10.5565/publmat_22180_12
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• Resumen

  • Theorems characterizing stable parabolic points are proved. Essentially, stability is equivalent to the fact that the generating function of the differomorphism, taking out the part which generates the identity, has a strict extremum at the fixed point. With these results, the study of the stability of fixed points of analytic area preserving mappings (APM) is ended . Some examples are included, specially the case of elliptic points whose ei-genvalues are cubic or fourth roots of unity.