Asymptoticity in General Systems

  • P. M. Salzberg
  • P. Seibert
Part of the NATO Conference Series book series (NATOCS, volume 5)


Modern trends toward extending Liapunov’s second method started with the work of D. Bushaw [6] on stability of abstract flows on uniform spaces, and of J. Auslander and P. Seibert [1–3] on stability of dynamical systems with respect to filters. Various theories following similar lines have been developed also by Nagy [10], Bushaw [5], Dana [7], Habets and Peiffer [9], Pelczar [11] and Rogers [12]. In [13–17], we have presented a theory of Liapunov stability under weakest assumptions: Stability is defined for a “system” consisting of a set endowed with a preorder (the “flow”) and two collections of subsets, or “quasifilters” (a kind of generalized neighborhood systems).


Event Space Uniform Space Liapunov Function Uniform Attraction Abstract Flow 
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Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • P. M. Salzberg
    • 1
  • P. Seibert
    • 1
  1. 1.Departamento de Matemática y Ciencias de la ComputaciónUniversidad Simón BolívarVenezuela

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