Skip to main content
Log in

Catastrophe theory

  • Published:
Synthese Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Bibliography

(i) Books

  1. M. Golubitsky and V. Guillemin, Stable Maps and Their Singularities, Springer-Verlag, New York, 1974.

    Google Scholar 

  2. M. M. Peixoto (ed.), Dynamical Systems, Proceedings of a symposium held Salvador, Brazil; Academic Press, New York and London, 1973.

    Google Scholar 

  3. Proceedings of the Liverpool Singularities Symposium I, 1971 (Springer Lecture Notes No. 192).

  4. Manifolds-Amsterdam 1970, Springer Lecture Notes No. 197.

  5. G. Wasserman, Stability of Unfoldings, Springer Lecture Notes No. 393.

  6. V. Poénaru, Analyse Différentielle, Springer Lecture Notes No. 371.

  7. R. Abraham and J. Robbin, Transversal Mappings and Flows, Benjamin, New York 1967.

    Google Scholar 

  8. S. Lang, Introduction to Differentiable Manifolds, Interscience, New York, 1962.

    Google Scholar 

  9. R. Thom, Stabilité structurelle et morphogénèse, Benjamin, 1972.

(ii) Articles (Initials such as DS or PSSLI refer to the books listed in (i).)

  1. V. I. Arnol'd, ‘Singularities of Smooth Maps’, Uspehi Mat. Nauk 23 (1968), 3–44, translated in Russian Math. Surveys (1969), pp. 1–43.

    Google Scholar 

  2. V. I. Arnol'd, (a) ‘Integrals of Rapidly Oscillating Functions and Singularities of Projections of Lagrangian Manifolds’, and (b) ‘Normal Forms for Functions Near Degenerate Critical Points, the Weyl Groups of Ak, Dk, Ek, and Lagrangian Singularities’, Funktional'nyi Analiz i Ego Prilozheniya (1972) 6; (a) in No. 3, pp. 61–62 and (b) in No. 4, pp. 3–25. Translation in Funct. Anal. and Applications (1973), pp. 222–223 and 254–272.

  3. N. A. Baas, ‘On the models of Thom in Biology and Morphogenesis’, Math. Biosci. 17 (1973), 173–187.

    Google Scholar 

  4. J. M. Boardman, ‘Singularities of Differentiable Mappings’, Publ. I.H.E.S., No. 33 (1967), pp. 21–57.

  5. A. Chenciner, ‘Travaux de Mather sur la stabilité topologique’, Sém. Bourbaki, exposé 424, Vol. 1972/1973, Springer Lecture Notes No. 382.

  6. J. Guckenheimer, ‘Catastrophes and Partial Differential Equations’, Ann. Inst. Fourier Grenoble 23, 2(1973), 31–59.

    Google Scholar 

  7. H. Hendriks, ‘La stratification “naturelle” de l'espace des fonctions différentiables réeles n'est pas la bonne’, C.R. Acad. Sci. Paris 274, série A(1972), pp. 618–620.

    Google Scholar 

  8. F. Latour, ‘Stabilité des champs d'applications différentiables; généralization d'un theorème de J. Mather’, C. R. Acad. Sci. Paris 268, série A(1969), pp. 1331–1334.

    Google Scholar 

  9. J. N. Mather, ‘Stability of C∞ Mappings I’, Ann. of Math. 87 (1968), pp. 89–104; II ibid. 89 (1969), pp. 254–291; III Publ. I.H.E.S. 35 (1969), 127–156; IV ibid. 37 (1970), pp. 223–248; V Advances in Math. 4 (1970), 301–335; and VI in PSSLI pp. 207–253.

    Google Scholar 

  10. J. N. Mather, ‘Notes on Topological Stability’, preprint, Harvard Univ., Cambridge, Massachusetts, 1970.

    Google Scholar 

  11. J. N. Mather, ‘Stratifications and Mappings’, in DS pp. 195–232.

    Google Scholar 

  12. V. Poénaru, ‘Un théorème des fonctions implicites pour les espaces d'applications C∞’, Publ. I.H.E.S. 38 (1978), 93–124.

    Google Scholar 

  13. F. Sergeraert, ‘Un théorème de fonctions implicites sur certains espaces de Fréchet et quelques applications’, Ann. Scient. Ec. Norm. Sup., 4th series, 5 (1972), 599–660.

    Google Scholar 

  14. R. Thom, ‘Les singularités des applications différentiables’, Ann. Inst. Fourier Grenoble 6 (1955–1956), 43–87.

    Google Scholar 

  15. R. Thom and H. I. Levine, ‘Singularities of Differentiable Mappings’, in PSSLI pp. 1–89.

  16. R. Thom, ‘Ensembles et morphismes stratifiés’, Bull. Amer. Math. Soc. 75 (1969), pp. 240–284.

    Google Scholar 

  17. R. Thom, ‘The Bifurcation Subset of a Space of Mappings’, in MA 1970 pp. 202–208.

  18. R. Thom, ‘Topological Models in Biology’, Topology 8 (1969), 313–335.

    Google Scholar 

  19. R. Thom, ‘Topologie et linguistique’, in Essays on Topology, Vol. dedicated to G. de Rham, Springer-Verlag, Berlin and New York, 1970.

    Google Scholar 

  20. R. Thom, ‘Language et catastrophes’, in DS pp. 619–654.

    Google Scholar 

  21. C. T. C. Wall, ‘Lectures on C∞ Stability and Classification’, in PLSSI pp. 178–206.

  22. H. Whitney, ‘On Singularities of Mappings of Euclidean Spaces I, Mappings of the Plane Into the Plane, Ann. of Math. 62 (1965), 374–410.

    Google Scholar 

  23. E. C. Zeeman, ‘Differential Equations for the Heartbeat and Nerve Impulse’, in DS pp. 683–741.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Work partially supported by NSF Grant No. GP-37488.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sussmann, H.J. Catastrophe theory. Synthese 31, 229–270 (1975). https://doi.org/10.1007/BF00485979

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00485979

Keywords

Navigation