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On dynamical systems of characteristic 0+

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Abstract

The purpose of this paper is to characterize planar dynamical systems satisfying certain stability criteria. The flows are characterized in terms of their critical points and a nontrivial example satisfying all of the properties obtained by Ahmad is constructed.

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References

  1. S. Ahmad, Dynamical systems of characteristic 0+,Pac. J. Math. 32 (1970), 561–574.

    Google Scholar 

  2. S. Ahmad, Strong attraction and classification of certain continuous flows,Math. Systems Theory,5 (1971), 157–163.

    Google Scholar 

  3. H. Antosiewicz andJ. Dugundji, Parallelizable flows and Liapunov's second method,Ann. of Math. 73 (1961), 543–555.

    Google Scholar 

  4. N. Bhatia, Criteria for dispersive flows,Math. Nachr. 32 (1960), 89–93.

    Google Scholar 

  5. N. Bhatia andO. Hajek, Local semi-dynamical systems,Lecture Notes in Math. No. 90, Springer-Verlag, New York, 1969.

    Google Scholar 

  6. N. Bhatia andO. Hajek, Theory of dynamical systems, Parts I and II, Technical Notes BN-599 and BN-606, University of Maryland (1969).

  7. O. Hajek,Dynamical Systems in the Plane, Academic Press, New York, 1968.

    Google Scholar 

  8. R. Knight, Dynamical systems of characteristic 0,Pacific J. Math. 41 (1972).

  9. R. Knight, Characterizations of Certain Classes of Planar Dynamical Systems, Ph.D. Dissertation, Oklahoma State University, 1971.

  10. V. Nemytskii andV. Stepanov,Qualitative Theory of Differential Equations, English Trans., Princeton Univ. Press, Princeton, New Jersey, 1960.

    Google Scholar 

  11. T. Ura, Sur le Courant Extérieur à une Région Invariante; Prolongements d'une Caracteristique et l'order de Stabilité,2 (1959), 143–200; nouv. edition 105–143.Funkcialaj Ekvacioj, Ser. internac.

    Google Scholar 

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Authors and Affiliations

  1. Mathematics Division, Northeast Missouri State University, 63501, Kirksville, Missouri, USA

    Ronald A. Knight

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  1. Ronald A. Knight
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Knight, R.A. On dynamical systems of characteristic 0+ . Math. Systems Theory 9, 368–377 (1975). https://doi.org/10.1007/BF01715362

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  • DOI: https://doi.org/10.1007/BF01715362

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