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Abstract

I had planned to give a comprehensive account of the results obtained by me and Dr. Szegö during the past few years together with related results of various authors in the field of dynamical systems. With the appearance of our lecture notes [1] this prospect is not too attractive now so that I would like to concentrate on a couple of problems and techniques which seem to hold promise. But first the following definition.

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References

  1. [1]
    N.P. Bhatia and G.P. Szegö, “Dynamical Systems: Stability Theory and Applications”, Lecture Notes in Mathematics No. 35, Springer-Verlag, Berlin-Heidelberg-New York, 1967.zbMATHCrossRefGoogle Scholar
  2. [2]
    V.V. Nemytskii and V.V. Stepanov, “Qualitative Theory of Differential Equations”, Princeton University Press, Princeton, New Jersey, 1960. Original Russian 1947.zbMATHGoogle Scholar
  3. [3]
    V.V. Nemytskii, Topological Problems of the Theory of Dynamical Systems, Uspehi Mat. Nauk., 4 (1949), 91–153 (Russian). English Translation: American Mathematical Society Translations No. 103 (1954)Google Scholar
  4. [4]
    H. Poincare, “Les methodes nouvelles de la mecaniques celeste”, Gauthier-Villars, Paris, 1892–1899. Reprint, Dover, New York.Google Scholar
  5. [5]
    G.D. Birkhoff, “Dynamical Systems”, American Mathematical Society Colloquium Publications, Vol. 9, New York, 1927 reprinted 1966Google Scholar
  6. [6]
    Taro Ura, Sur le courant exterieur à une region invariante; Prolongements d’une caracteristique et l’ordre de stabilite, Funkcialay Ekvakioj, 2 (1959), 143–200MathSciNetzbMATHGoogle Scholar
  7. [7]
    I. Kimura and Taro Ura, Sur le courant exterieur à une region invariante: Theoreme de Bendixon, Comment. Math. Univers. Sancti Pauli, Vol. 8 (1960), 23–29MathSciNetGoogle Scholar
  8. [8]
    N.P. Bhatia, Weak Attractors in Dynamical Systems, Bol Soc. Mat.Mex., 11 (1966), 56–64MathSciNetGoogle Scholar
  9. [9]
    Paul Fallone, Properties of asymptotically stable sets and their regions of attraction, Ph.D. Thesis, Department of Mathematics, Western Reserve University, Cleveland, Ohio, May 1967Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1969

Authors and Affiliations

  • Nam P. Bhatia

There are no affiliations available

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