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Liapunov direct method in approaching bifurcation problems

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Summary

A concept of total stability for continuous or discrete dynamical systems and a generalized definition of bifurcation are given: it is possible to show the link between an abrupt change of the asymptotic behaviour of a family of flows and the arising of new invariant sets, with determined asymptotic properties. The theoretical results are a contribution to the study of the behaviour of flows near an invariant compact set. They are obtained by means of an extension of Liapunov's direct method.

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A Dario Graffi nel suo 70° compleanno

Entrata in Redazione il 9 febbraio 1975.

Work performed under the auspices of the Italian Council of Research (C.N.R.).

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Marchetti, F., Negrini, P., Salvadori, L. et al. Liapunov direct method in approaching bifurcation problems. Annali di Matematica 108, 211–226 (1976). https://doi.org/10.1007/BF02413955

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Keywords

  • Dynamical System
  • Asymptotic Behaviour
  • Theoretical Result
  • Abrupt Change
  • Asymptotic Property