On deducing the presence of catastrophes
Mathématiques et sciences humaines, Tome 64 (1978), pp. 71-99.
@article{MSH_1978__64__71_0,
     author = {Poston, Tim},
     title = {On deducing the presence of catastrophes},
     journal = {Math\'ematiques et sciences humaines},
     pages = {71--99},
     publisher = {Ecole Pratique des hautes \'etudes, Centre de math\'ematique sociale et de statistique},
     volume = {64},
     year = {1978},
     mrnumber = {538884},
     zbl = {0411.00016},
     language = {en},
     url = {http://www.numdam.org/item/MSH_1978__64__71_0/}
}
TY  - JOUR
AU  - Poston, Tim
TI  - On deducing the presence of catastrophes
JO  - Mathématiques et sciences humaines
PY  - 1978
SP  - 71
EP  - 99
VL  - 64
PB  - Ecole Pratique des hautes études, Centre de mathématique sociale et de statistique
UR  - http://www.numdam.org/item/MSH_1978__64__71_0/
LA  - en
ID  - MSH_1978__64__71_0
ER  - 
%0 Journal Article
%A Poston, Tim
%T On deducing the presence of catastrophes
%J Mathématiques et sciences humaines
%D 1978
%P 71-99
%V 64
%I Ecole Pratique des hautes études, Centre de mathématique sociale et de statistique
%U http://www.numdam.org/item/MSH_1978__64__71_0/
%G en
%F MSH_1978__64__71_0
Poston, Tim. On deducing the presence of catastrophes. Mathématiques et sciences humaines, Tome 64 (1978), pp. 71-99. http://www.numdam.org/item/MSH_1978__64__71_0/

[1] R. Abraham & J.W. Robbin, Transversal Mappings and Flows, Benjamin, N.Y. 1967. | MR | Zbl

[2] V.I. Arnol'D, Wave front evolution and equivariant Morse Lemma, Comm. Pure Appl. Math. 29 (1976) 557-582. | MR | Zbl

[3] J. Chazarain, Solutions asymptotiques et caustiques, in Rencontre de Cargèse sur les singularités et leurs applications (ed. F. Pham) publ. Math. Dept. Univ. Nice 1975.

[4] R. Courant & H. Robbins, What Is Mathematics?, Oxford University Press 1941. | JFM | MR | Zbl

[5] N.F. Dixon, On the Psychology of Military Incompetence, Johnathan Cape, London 1976.

[6] A.S. Eddington, Gravitation and the Principle of Relativity, Royal Institution Discourse 1918.

[7] P.J. Holmes & D.A. Rand, The bifurcations of Duffing's equation: an application of catastrophe theory, J. Sound Vib.44 (1976) 237-253. | Zbl

[8] L. Van Hove, The occurrence of singularities in the elastic frequency distribution of a crystal, Phys. Rev. 89 (1953), 1189-1193. | MR | Zbl

[9] C.A. Isnard & E.C. Zeeman, Some models from catastrophe theory in the social sciences, in Use of Models in the Social Sciences (ed. L. Collins), Tavistock, London 1975.

[10] J.J. Kozak and C.J. Benham, Denaturation; an example of a catastrophe I, Proc. Nat. Acad. Sci. USA 71 (1974), 1977-1981. (The 'review article' [31] was written without awareness of parts II, III in J. Theor. Biol. 63 (1976) 125-149, 66 (1977) 679-693 which had already dealt with those objections in [31] not dependent on misrepresentation.) | Zbl

[11] H. Kurland & J. Robbin, Infinite codimension and Transversality, in Dynamical Systems - Warwick 1974 (ed. A. Manning), Lecture Notes in Math. 468, Springer, Berlin 1975, 135-150. | MR | Zbl

[12] L.D. Landau & E.M. Lifshitz, Statistical Physics, 2nd English edition (trans Peierls & Peierls), Pergamon, Oxford 1959. | MR | Zbl

[13] K. Lorenz, On Aggression, Bantam Books, N.Y. 1967.

[14] R.J. Magnus & T. Poston, On the full unfolding of the von Kármán equation at a double eigenvalue, Math. Report 109, Battelle, Geneva 1977.

[15] A. Du Plessis, Maps without certain singularities, to appear in Comm. Math. Helv. | MR | Zbl

[16] T. Poston, Au courant with differential equations, Manifold 18 (1976) 6-9.

[17] T. Poston, The elements of catastrophe theory or The honing of Occam's razor, to appear in Transformations: Mathematical Approaches to Culture Change (eds K.L. Cooke and A.C. Renfrew), Academic Press, N.Y. 1978.

[18] T. Poston & I.N. Stewart, Taylor Expansions and Catastrophes, Research Notes in Math. 7, Pitman, London & S. Francisco 1976. | MR | Zbl

[19] T. Poston & I.N. Stewart, Catastrophe Theory and its Applications, Pitman, London & S. Francisco 1978. | Zbl

[20] M. Spivak, Calculus on Manifolds, Benjamin, N.Y. 1965. | MR | Zbl

[21] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967) 747-817. | MR | Zbl

[22] I.N. Stewart, The Seven Elementary Catastrophes, New Scientist 68 (1975) , 447-454.

[23] I.N. Stewart, Catastrophe Theory, Special Supplement to Britannica Book of the Year 1977.

[24] H.J. Sussmann, Some properties of vector fields that are not altered by small perturbations, J. Diff. Eq. 20 (1976) no 2, 292-315. | MR | Zbl

[25] H.J. Sussmann, Catastrophe theory - a preliminary critical study, PSA 1976 vol. 1 (eds. F. Suppe & P.D. Asquith), Phil. Sci. Assoc., East Lansing, Michigan 1976.

[26] H.J. Sussmann & R.S. Zahler, Catastrophe theory as applied to the social and biological Sciences : a critique, to appear in Synthèse. All quotations are from the widely circulated preprint, Rutgers Univ. Math. Dept., Feb. 1977. | MR | Zbl

[27] H.J. Sussmann & R.S. Zahler, Catastrophe theory: mathematics misused, The Sciences 17 no 6 (1977) 20-23.

[28] R. Thom, Answer to Christopher Zeeman's reply, in Dynamical Systems - Warwick 1974 (ed. A. Manning), Lecture Notes in Math. 468, Springer, Berlin 1975, 384-389. | MR

[29] R. Thom, Structural stability catastrophe theory, and applied mathematics, SIAM Review 19, 189-201, 1977. | MR | Zbl

[30] A.E.R. Woodcock & T. Poston, A Geometrical Study of the Elementary Catastrophes, Lecture Notes in Math. 373, Springer, Berlin 1974. | Zbl

[31] R.S. Zahler & H.J. Sussmann, Claims and accomplishments of applied catastrophe theory, Nature 269 (1977), 759-763. Letters pointing out many errors, misquotations etc. are in ibid. 270 (1977), 381-384, 658, and a reply by Zahler with some new ones in 271 (1978), 401.

[32] E.C. Zeeman, Differential equations for the heartbeat and nervous impulse, in Towards a Theoretical Biology IV (ed. C.H. Waddington), Edinburgh Univ. Press, 1972, 8-67, Dynamical Systems (ed. M.M. Peixoto), Academic Press, N.Y. 1973, and [35] 81-140. | MR

[33] E.C. Zeeman, Primary and secondary waves in developmental biology, AAAS 1974, Some Mathematical Questions in Biology VIII, Lectures on Mathematics in the Life Sciences 7, Amer. Math. Soc., Providence R.I. 1974, 69-161, and [35] 141-233. | MR | Zbl

[34] E.C. Zeeman, On the unstable behaviour of stock exchanges, J. Math. Econ. 1 (1974) 39-49, and [35], 361-371. | MR | Zbl

[35] E.C. Zeeman, Catastrophe Theory: Selected Papers (1972-1977), Addison-Wesley, N.Y. 1977. | MR | Zbl

[36] E.C. Zeeman, A boundary value problem involving cusps, to appear.

See also I.N. Stewart and T. Poston, The Catastrophe Theory Controversy, to appear in the New Scientist, and the September 1978 special 'Catastrophe Theory' issue of Behavioral Science, where further arguments for catastrophe modelling are variously developed.