Abstract
In this paper we consider analytic area preserving mappings (APM) near a fixed point. If the fixed point is parabolic a criterion is given which ensures the existence of invariant curves and, hence, stability. An heuristic discussion of the limit of the stability region completes the paper.
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References
Arnold,V.I.,Avez,A.: Ergodic problems of classical mechanics. Benjamin (1968).
Bartlett,J.: Global stability of area preserving mappings, in Long-time predictions in dynamics, ed.V.Szebehely and B.D.Tapley. Reidel (1976),pp.99–110.
Chirikov,B.D.,Izraelev,F.M.: Some numerical experiments with a nonlinear mapping: stochastic component, in Transformations ponctuelles et leurs applications, Colloque international du C.N.R.S. no229 (1973), pp.409–428.
Engel, W.: Ganze Cremona-Transformationen von Primzahlgrad in der Ebene, Math. Annalen 136, 319–325 (1958).
Levi-Civita, T.: Sopra alcuni criteri di instabilità , Annali di Matematica, Ser.III, 5, 221–307 (1901).
Siegel,C.L.,Moser,J.K.: Lectures on Celestial Mechanics. Springer (1971).
Simó,C.: Una nota sobre las aplicaciones cuadráticas que conservan área, in Actas V Congreso de Matemáticos de Expresión Latina, Palma 1977, pp.361–369.
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© 1980 Springer-Verlag
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Simó, C. (1980). Invariant curves near parabolic points and regions of stability. In: Nitecki, Z., Robinson, C. (eds) Global Theory of Dynamical Systems. Lecture Notes in Mathematics, vol 819. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087005
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DOI: https://doi.org/10.1007/BFb0087005
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