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Topological equivalence in bifurcation theory

Part of the Lecture Notes in Mathematics book series (LNM,volume 799)

Keywords

  • Banach Space
  • Normal Form
  • Hopf Bifurcation
  • Bifurcation Point
  • Singularity Theory

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References

  1. ARKERYD, L. Catastrophe theory in Hilbert space, Tech. Report, Math. Dept., University of Gothenburg (1977).

    Google Scholar 

  2. Thom's theorem for Banach spaces, J. Lon. Math. Soc. (To appear).

    Google Scholar 

  3. CHILLINGWORTH, D.R.J. A global genericity theorem for bifurcation in variational problems, Preprint, Math. Dept., Univ. of Southampton (1978).

    Google Scholar 

  4. CHOW, S.-N., HALE, J.K. and MALLET-PARET, J. Applications of generic bifurcation, Arch. Rat. Mech. Anal. 59(1975), 159–188

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Ibid Applications of generic bifurcation, Arch. Rat. Mech. Anal. 62(1976), 209–235.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. CRANDALL, H.G. and RABINOWITZ, P.H. Bifurcation from simple eigenvalues, J. Funct. Anal. 8(1971), 321–340.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. GUIMARÃES, L.C. Contact equivalence and bifurcation theory, Thesis, University of Southampton (1978).

    Google Scholar 

  8. KUO, T.-C. Characterization of v-sufficiency of jets, Topology, 11(1972), 115–131.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. McLEOD, J.B. and SATTINGER, D.H. Loss of stability and bifurcation at a double eigenvalue, J. Funct. Anal. 14(1973), 62–84.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. MAGNUS, R.J. On universal unfoldings of certain real functions on a Banach space, Math. Proc. Cam. Phil. Soc. 81(1977), 91–95.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Determinacy in a class of germs on a reflexive Banach space, Math. Proc. Cam. Phil. Soc. 84(1978), 293–302.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Universal unfoldings in Banach spaces: reduction and stability, Battelle-Geneva Math. Report 107(1977) (To appear in Math. Proc. Cam. Phil. Soc.).

    Google Scholar 

  13. On the local structure of the zero set of a Banach space valued mapping, J. Funct. Anal. 22(1976), 58–72.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. The reduction of a vector-valued function near a critical point, Battelle-Geneva Math. Report 93(1975).

    Google Scholar 

  15. SHEARER, M. Small solutions of a non-linear equation in Banach space for a degenerate case, Proc. Royal Soc. Edinburgh, 79A (1977). 58–73.

    MathSciNet  MATH  Google Scholar 

  16. Bifurcation in the neighbourhood of a non-isolated singular point, Israel J. Math. 30(1978), 363–381.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. BUCHNER, M., MARSDEN, J. and SCHECTER, S. Differential topology and singularity theory in the solution of non-linear equations (preliminary version), University of California, Berkeley.

    Google Scholar 

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© 1980 Springer-Verlag

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Magnus, R. (1980). Topological equivalence in bifurcation theory. In: Izé, A.F. (eds) Functional Differential Equations and Bifurcation. Lecture Notes in Mathematics, vol 799. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089318

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  • DOI: https://doi.org/10.1007/BFb0089318

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09986-4

  • Online ISBN: 978-3-540-39251-4

  • eBook Packages: Springer Book Archive