Stability and Bifurcation Problems

  • L. Salvadori
  • F. Visentin
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 387)


The course deals with the stability theory (Parts I,II) and its connection with the bifurcation theory (Part III). Some more recent approaches to stability problems are described, for example by methods which make use of suitable one parameter families of Liapunov functions. Several applications to conservative as well as dissipative mechanical systems with a finite number of degrees of freedom are given. The connection between stability and bifurcation is due to the fact that bifurcation phenomena often occur because of exchange of stability properties under perturbations of the governing equations. Thus stability arguments, in particular appropriate Liapunov functions, may be used not only to analyze the qualitative behavior of the flow near the bifurcating sets, but also to prove the existence of these sets.


Periodic Orbit Function Versus Asymptotic Stability Differential System Positive Real Part 


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Copyright information

© Springer-Verlag Wien 1998

Authors and Affiliations

  • L. Salvadori
    • 1
  • F. Visentin
    • 2
  1. 1.University of TrentoTrentoItaly
  2. 2.University of Naples “Federico II”NaplesItaly

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