Abstract
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).
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References
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Salzberg, P.M., Seibert, P. (1978). Asymptoticity in General Systems. In: Klir, G.J. (eds) Applied General Systems Research. NATO Conference Series, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0555-3_27
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DOI: https://doi.org/10.1007/978-1-4757-0555-3_27
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