Skip to main content
SpringerLink
Log in

Bifurcation from a manifold

  • Conference paper
  • First Online:
Singularity Theory and its Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1463))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arnol’d, V.I., Indices of singular points of 1-forms on a manifold with boundary, convolution of invariants of reflection groups and singular projections of smooth surfaces, Russian Math. Surveys 34 (1979), 1–42.

    Article  MATH  Google Scholar 

  2. Ambrosetti, A., Coti Zelati, V. and Ekeland, I., Symmetry breaking in Hamiltonian systems, J. Diff. Eqns. 67 (1987), 165–184.

    Article  MathSciNet  MATH  Google Scholar 

  3. Bröcker, Th. and Lander, L., Differentiable germs and catastrophes, London Math. Soc. Lecture Notes 17, Cambridge University Press 1975.

    Google Scholar 

  4. Bruce, J.W., Canonical stratifications: the simple singularities, Math. Proc. Cambridge Philos. Soc. 88 (1980), 265–272.

    Article  MathSciNet  MATH  Google Scholar 

  5. Bruce, J.W., The duals of generic hypersurfaces, Math. Scand. 49 (1981), 36–60.

    MathSciNet  MATH  Google Scholar 

  6. Bruce, J.W., On singularities, envelopes and elementary differential geometry, Math. Proc. Cambridge Philos. Soc. 89 (1981), 43–48.

    Article  MathSciNet  MATH  Google Scholar 

  7. Bruce, J.W., Generic reflections and projections of surfaces, Math. Scand. 54 (1984), 262–278.

    MathSciNet  MATH  Google Scholar 

  8. Bruce, J.W., Seeing — the mathematical viewpoint, Math. Intelligencer 6 (1984), 18–25.

    Article  MathSciNet  MATH  Google Scholar 

  9. Bruce, J.W., Geometry of singular sets, Math. Proc. Cambridge Philos. Soc. 106 (1989), 495–509.

    Article  MathSciNet  MATH  Google Scholar 

  10. Bruce, J.W. and Giblin, P.J., On real simple singularities, Math. Proc. Cambridge Philos. Soc. 88 (1980), 273–279.

    Article  MathSciNet  MATH  Google Scholar 

  11. Bruce, J.W. and Giblin, P.J., Curves and singularities, Cambridge University Press 1984.

    Google Scholar 

  12. Chillingworth, D.R.J., Bifurcation from an orbit of symmetry, in Singularities and Dynamical Systems, S.N. Pnevmatikos (ed.), pp. 285–294, North-Holland, Amsterdam 1985.

    Google Scholar 

  13. Chillingworth, D.R.J., The ubiquitous astroid, in Proc. Int. Symp. on The Physics of Structure Formation: Theory and Simulation, Institut für Informationsverarbeitung, Universität Tübingen, 1986, W. Güttinger and G. Dangelmayr (eds.), pp. 372–386, Springer-Verlag, Berlin 1987.

    Chapter  Google Scholar 

  14. Chillingworth, D.R.J., Marsden, J.E. and Wan, Y.-H., Symmetry and bifurcation in three-dimensional elasticity, Part I: Arch. Rat. Mech. Anal. 80 (1982), 295–331, Part II: Arch. Rat. Mech. Anal. 8 (1983), 363–395.

    Article  MathSciNet  MATH  Google Scholar 

  15. Chow, S.-N. and Hale, J.K., Methods of bifurcation theory, Springer-Verlag, New York, 1982.

    Book  MATH  Google Scholar 

  16. Dancer, E.N., On the existence of bifurcating solutions in the presence of symmetries, Proc. Roy. Soc. Edinburgh 85A (1980), 321–336.

    Article  MathSciNet  MATH  Google Scholar 

  17. Dancer, E.N., The G-invariant implicit function theorem in infinite dimensions, Proc. Roy. Soc. Edinburgh 92A (1982), 13–30.

    Article  MathSciNet  MATH  Google Scholar 

  18. Dancer, E.N., Perturbation of zeros in the presence of symmetries, J. Austral. Math. Soc. (Ser. A) 36 (1984), 106–125.

    Article  MathSciNet  MATH  Google Scholar 

  19. Golubitsky, M. and Guillemin, V., Stable mappings and their singularities, Springer-Verlag, New York 1973.

    Book  MATH  Google Scholar 

  20. Golubsky, M. and Schaeffer, D., Imperfect bifurcation in the presence of symmetry, Common. Math. Phys. 67 (1979), 205–232.

    Article  MathSciNet  MATH  Google Scholar 

  21. Golubitsky, M., Stewart, I. and Schaeffer, D.G., Singularities and Groups in Bifurcation Theory, Vols. I, II., Springer-Verlag, New York, 1985, 1988.

    Book  MATH  Google Scholar 

  22. Hale, J.K. and Taboas, P.Z., Interaction of damping and forcing in a second order equation, Nonlin. Anal. Th. Meth. Appl. 2 (1978), 77–84.

    Article  MathSciNet  MATH  Google Scholar 

  23. Looijenga, E.J.N., Structural stability of smooth families of C∞ functions, Thesis, Univ. Amsterdam, 1974.

    Google Scholar 

  24. Marsden, J.E., Qualitative methods in bifurcation theory, Bull. Amer. Math. Soc. 84 (1978), 1125–1148.

    Article  MathSciNet  MATH  Google Scholar 

  25. Mather, J.N., Generic projections, Ann. Math. (2), (1973), 226–245.

    Google Scholar 

  26. Magnus, R.J., On perturbations of a translationally invariant differential equation, Proc. Roy. Soc. Edinburgh 110A (1988), 1–25.

    Article  MathSciNet  MATH  Google Scholar 

  27. Reeken, M., Stability of critical points under small perturbations, Part I: Topological theory, Manuscripta Math. 7 (1972), 387–411.

    Article  MathSciNet  MATH  Google Scholar 

  28. Vanderbauwhede, A., Symmetry and bifurcations near families of solutions, J. Diff. Eqns. 36 (1980), 173–187.

    Article  MathSciNet  MATH  Google Scholar 

  29. Vanderbauwhede, A., Local Bifurcation and Symmetry, Research Notes in Math. 75, Pitman, London 1982.

    MATH  Google Scholar 

  30. Wall, C.T.C., Geometric properties of generic differentiable manifolds, in: Geometry and Topology III, Lecture Notes in Math. 597, Springer-Verlag, Berlin 1976.

    Google Scholar 

  31. Weinstein, A., Perturbation of periodic manifolds of Hamiltonian systems, Bull. Amer. Math. Soc. 77 (1971), 814–818.

    Article  MathSciNet  MATH  Google Scholar 

  32. Wan, Y.-H. and Marsden, J.E., Symmetry and bifurcation in three-dimensional elasticity, Part III, Arch. Rat. Mech. Anal. 84 (1983), 203–233.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. David Chillingworth
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Mark Roberts Ian Stewart

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Chillingworth, D. (1991). Bifurcation from a manifold. In: Roberts, M., Stewart, I. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085424

Download citation

  • DOI: https://doi.org/10.1007/BFb0085424

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53736-6

  • Online ISBN: 978-3-540-47047-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation