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Stability of parabolic points of area preserving analytic diffeomorphisms
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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.
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SIMÓ, Carles. Stability of parabolic points of area preserving analytic diffeomorphisms. Publicacions Matemàtiques. 1980. Vol. 22, num. 67-70. ISSN 0214-1493. [consulted: 6 of June of 2026]. Available at: https://hdl.handle.net/2445/132430