Bibliography
(i) Books
M. Golubitsky and V. Guillemin, Stable Maps and Their Singularities, Springer-Verlag, New York, 1974.
M. M. Peixoto (ed.), Dynamical Systems, Proceedings of a symposium held Salvador, Brazil; Academic Press, New York and London, 1973.
Proceedings of the Liverpool Singularities Symposium I, 1971 (Springer Lecture Notes No. 192).
Manifolds-Amsterdam 1970, Springer Lecture Notes No. 197.
G. Wasserman, Stability of Unfoldings, Springer Lecture Notes No. 393.
V. Poénaru, Analyse Différentielle, Springer Lecture Notes No. 371.
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S. Lang, Introduction to Differentiable Manifolds, Interscience, New York, 1962.
R. Thom, Stabilité structurelle et morphogénèse, Benjamin, 1972.
(ii) Articles (Initials such as DS or PSSLI refer to the books listed in (i).)
V. I. Arnol'd, ‘Singularities of Smooth Maps’, Uspehi Mat. Nauk 23 (1968), 3–44, translated in Russian Math. Surveys (1969), pp. 1–43.
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.
N. A. Baas, ‘On the models of Thom in Biology and Morphogenesis’, Math. Biosci. 17 (1973), 173–187.
J. M. Boardman, ‘Singularities of Differentiable Mappings’, Publ. I.H.E.S., No. 33 (1967), pp. 21–57.
A. Chenciner, ‘Travaux de Mather sur la stabilité topologique’, Sém. Bourbaki, exposé 424, Vol. 1972/1973, Springer Lecture Notes No. 382.
J. Guckenheimer, ‘Catastrophes and Partial Differential Equations’, Ann. Inst. Fourier Grenoble 23, 2(1973), 31–59.
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.
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.
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.
J. N. Mather, ‘Notes on Topological Stability’, preprint, Harvard Univ., Cambridge, Massachusetts, 1970.
J. N. Mather, ‘Stratifications and Mappings’, in DS pp. 195–232.
V. Poénaru, ‘Un théorème des fonctions implicites pour les espaces d'applications C∞’, Publ. I.H.E.S. 38 (1978), 93–124.
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.
R. Thom, ‘Les singularités des applications différentiables’, Ann. Inst. Fourier Grenoble 6 (1955–1956), 43–87.
R. Thom and H. I. Levine, ‘Singularities of Differentiable Mappings’, in PSSLI pp. 1–89.
R. Thom, ‘Ensembles et morphismes stratifiés’, Bull. Amer. Math. Soc. 75 (1969), pp. 240–284.
R. Thom, ‘The Bifurcation Subset of a Space of Mappings’, in MA 1970 pp. 202–208.
R. Thom, ‘Topological Models in Biology’, Topology 8 (1969), 313–335.
R. Thom, ‘Topologie et linguistique’, in Essays on Topology, Vol. dedicated to G. de Rham, Springer-Verlag, Berlin and New York, 1970.
R. Thom, ‘Language et catastrophes’, in DS pp. 619–654.
C. T. C. Wall, ‘Lectures on C∞ Stability and Classification’, in PLSSI pp. 178–206.
H. Whitney, ‘On Singularities of Mappings of Euclidean Spaces I, Mappings of the Plane Into the Plane, Ann. of Math. 62 (1965), 374–410.
E. C. Zeeman, ‘Differential Equations for the Heartbeat and Nerve Impulse’, in DS pp. 683–741.
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Work partially supported by NSF Grant No. GP-37488.
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Sussmann, H.J. Catastrophe theory. Synthese 31, 229–270 (1975). https://doi.org/10.1007/BF00485979
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DOI: https://doi.org/10.1007/BF00485979