On deducing the presence of catastrophes

Tim Poston

Mathématiques et Sciences Humaines (1978)

  • Volume: 64, page 71-99
  • ISSN: 0987-6936

How to cite


Poston, Tim. "On deducing the presence of catastrophes." Mathématiques et Sciences Humaines 64 (1978): 71-99. <http://eudml.org/doc/94219>.

author = {Poston, Tim},
journal = {Mathématiques et Sciences Humaines},
keywords = {catastrophes theory},
language = {eng},
pages = {71-99},
publisher = {Ecole Pratique des hautes études, Centre de mathématique sociale et de statistique},
title = {On deducing the presence of catastrophes},
url = {http://eudml.org/doc/94219},
volume = {64},
year = {1978},

AU - Poston, Tim
TI - On deducing the presence of catastrophes
JO - Mathématiques et Sciences Humaines
PY - 1978
PB - Ecole Pratique des hautes études, Centre de mathématique sociale et de statistique
VL - 64
SP - 71
EP - 99
LA - eng
KW - catastrophes theory
UR - http://eudml.org/doc/94219
ER -


  1. [1] R. Abraham & J.W. Robbin, Transversal Mappings and Flows, Benjamin, N.Y.1967. Zbl0171.44404MR240836
  2. [2] V.I. Arnol'd, Wave front evolution and equivariant Morse Lemma, Comm. Pure Appl. Math.29 (1976) 557-582. Zbl0343.58003MR436200
  3. [3] J. Chazarain, Solutions asymptotiques et caustiques, in Rencontre de Cargèse sur les singularités et leurs applications (ed. F. Pham) publ. Math. Dept. Univ. Nice1975. 
  4. [4] R. Courant & H. Robbins, What Is Mathematics?, Oxford University Press1941. Zbl0060.12302MR5358JFM67.0001.05
  5. [5] N.F. Dixon, On the Psychology of Military Incompetence, Johnathan Cape, London1976. 
  6. [6] A.S. Eddington, Gravitation and the Principle of Relativity, Royal Institution Discourse1918. 
  7. [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. Zbl0337.34049
  8. [8] L. van Hove, The occurrence of singularities in the elastic frequency distribution of a crystal, Phys. Rev.89 (1953), 1189-1193. Zbl0050.23605MR56512
  9. [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, London1975. 
  10. [10] J.J. Kozak and C.J. Benham, Denaturation; an example of a catastrophe I, Proc. Nat. Acad. Sci. USA71 (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.) Zbl0289.92005
  11. [11] H. Kurland & J. Robbin, Infinite codimension and Transversality, in Dynamical Systems - Warwick 1974 (ed. A. Manning), Lecture Notes in Math. 468, Springer, Berlin1975, 135-150. Zbl0317.58011MR649273
  12. [12] L.D. Landau & E.M. Lifshitz, Statistical Physics, 2nd English edition (trans Peierls & Peierls), Pergamon, Oxford1959. Zbl0080.19702MR586944
  13. [13] K. Lorenz, On Aggression, BantamBooks, N.Y.1967. 
  14. [14] R.J. Magnus & T. Poston, On the full unfolding of the von Kármán equation at a double eigenvalue, Math. Report109, Battelle, Geneva1977. 
  15. [15] A. du Plessis, Maps without certain singularities, to appear in Comm. Math. Helv. Zbl0313.58010MR397779
  16. [16] T. Poston, Au courant with differential equations, Manifold18 (1976) 6-9. 
  17. [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. [18] T. Poston & I.N. Stewart, Taylor Expansions and Catastrophes, Research Notes in Math. 7, Pitman, London & S. Francisco1976. Zbl0335.58008MR494231
  19. [19] T. Poston & I.N. Stewart, Catastrophe Theory and its Applications, Pitman, London & S. Francisco1978. Zbl0382.58006
  20. [20] M. Spivak, Calculus on Manifolds, Benjamin, N.Y.1965. Zbl0141.05403MR209411
  21. [21] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc.73 (1967) 747-817. Zbl0202.55202MR228014
  22. [22] I.N. Stewart, The Seven Elementary Catastrophes, New Scientist68 (1975) , 447-454. 
  23. [23] I.N. Stewart, Catastrophe Theory, Special Supplement to Britannica Book of the Year1977. 
  24. [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. Zbl0346.49036MR394756
  25. [25] H.J. Sussmann, Catastrophe theory - a preliminary critical study, PSA1976 vol. 1 (eds. F. Suppe & P.D. Asquith), Phil. Sci. Assoc., East Lansing, Michigan1976. 
  26. [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. Zbl0389.92002MR495176
  27. [27] H.J. Sussmann & R.S. Zahler, Catastrophe theory: mathematics misused, The Sciences17 no 6 (1977) 20-23. 
  28. [28] R. Thom, Answer to Christopher Zeeman's reply, in Dynamical Systems - Warwick 1974 (ed. A. Manning), Lecture Notes in Math. 468, Springer, Berlin1975, 384-389. MR649921
  29. [29] R. Thom, Structural stability catastrophe theory, and applied mathematics, SIAM Review19, 189-201, 1977. Zbl0447.58010MR451284
  30. [30] A.E.R. Woodcock & T. Poston, A Geometrical Study of the Elementary Catastrophes, Lecture Notes in Math. 373, Springer, Berlin1974. Zbl0279.58004
  31. [31] R.S. Zahler & H.J. Sussmann, Claims and accomplishments of applied catastrophe theory, Nature269 (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. [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. MR342207
  33. [33] E.C. Zeeman, Primary and secondary waves in developmental biology, AAAS1974, 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. Zbl0317.92002MR484531
  34. [34] E.C. Zeeman, On the unstable behaviour of stock exchanges, J. Math. Econ.1 (1974) 39-49, and [35], 361-371. Zbl0297.90002MR418874
  35. [35] E.C. Zeeman, Catastrophe Theory: Selected Papers (1972-1977), Addison-Wesley, N.Y.1977. Zbl0398.58012MR474383
  36. [36] E.C. Zeeman, A boundary value problem involving cusps, to appear. 
  37. 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. 

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