Proceedings of the Japan Academy

A remark on the flow near a compact invariant set

Jirō Egawa

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Article information

Source
Proc. Japan Acad., Volume 49, Number 4 (1973), 247-251.

Dates
First available in Project Euclid: 20 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195519370

Digital Object Identifier
doi:10.3792/pja/1195519370

Mathematical Reviews number (MathSciNet)
MR0336722

Zentralblatt MATH identifier
0273.34029

Subjects
Primary: 54H20: Topological dynamics [See also 28Dxx, 37Bxx]
Secondary: 34C35

Citation

Egawa, Jirō. A remark on the flow near a compact invariant set. Proc. Japan Acad. 49 (1973), no. 4, 247--251. doi:10.3792/pja/1195519370. https://projecteuclid.org/euclid.pja/1195519370


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References

  • [1] N. P. Bhatia: Asymptotic recurrence and Dynamical Flow near a compact minimal set. Seminar on Differential Equations and Dynamical Systems. II. Lecture Notes in Mathematics, Vol. 144, 22-29. Springer Verlag, Berlin Heidelberg, New York (1970).
    Mathematical Reviews (MathSciNet): MR388360
    Zentralblatt MATH: 0213.36704
  • [2] N. P. Bhatia: Attraction and nonsaddle sets in dynamical systems. J. Diff. Eqs., 8, 229-249 (1970).
    Mathematical Reviews (MathSciNet): MR268481
    Zentralblatt MATH: 0207.08803
    Digital Object Identifier: doi:10.1016/0022-0396(70)90003-3
  • [3] D. Desbrow: On unstable invariant sets. Funkcial. Ekvac, 13, 109-126 (1970).
    Mathematical Reviews (MathSciNet): MR276951
    Zentralblatt MATH: 0227.54040
  • [4] N. N. Nemytskii and V. V. Stepanov: Qualitative theory of differential equations. Princeton Univ. Press, Princeton, N.J. (1960).
    Mathematical Reviews (MathSciNet): MR121520
    Zentralblatt MATH: 0089.29502
  • [5] T. Saito: Isolated minimal sets. Funkcial. Ekvac, 11, 155-167 (1968).
    Mathematical Reviews (MathSciNet): MR248417
    Zentralblatt MATH: 0186.56603
  • [6] T. Saito: On a compact invariant set isolated from minimal sets. Funkcial. Ekvac, 12, 193-204 (1969).
    Mathematical Reviews (MathSciNet): MR258010
    Zentralblatt MATH: 0184.48202
  • [7] T. Ura and I. Kimura: Sur le courant exterieur a une region invariante. Theoreme de Bendixson. Comm. Math. Univ, Sancti Pauli, 8, 23-39 (1960).
    Mathematical Reviews (MathSciNet): MR120428
    Zentralblatt MATH: 0117.16103
  • [8] T. Ura: On the flow outside a closed invariant set, stability, relative stability and saddle sets. Contr. Diff. Eqs. Ill, 249-294 (1964).
    Mathematical Reviews (MathSciNet): MR163018
    Zentralblatt MATH: 0161.28803

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