Book Review
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MathSciNet review:
1567142
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Book Information:
Authors:
Tim Poston and
Ian Stewart
Title:
Catastrophe theory and its applications
Additional book information:
Surveys and Reference Works in Mathematics, Pitman, London, 1978, xviii + 491 pp., $50.00.
V. I. Arnol′d, Singularities, bifurcations and catastrophes, Fiz.-Mat. Spis. BЪlgar. Akad. Nauk. 27(60) (1985), no. 1, 25–48 (Bulgarian). Translated from the Russian by E. Khorozov. MR 801647
M. V. Berry, Semi-classical mechanics in phase space: a study of Wigner’s function, Philos. Trans. Roy. Soc. London Ser. A 287 (1977), no. 1343, 237–271. MR 489464, DOI 10.1098/rsta.1977.0145
David Chillingworth, Elementary catastrophe theory, Bull. Inst. Math. Appl. 11 (1975), no. 8, 155–159. MR 494223
James Callahan, Singularities and plane maps, Amer. Math. Monthly 81 (1974), 211–240. MR 353336, DOI 10.2307/2319521
Martin Golubitsky, An introduction to catastrophe theory and its applications, SIAM Rev. 20 (1978), no. 2, 352–387. MR 470984, DOI 10.1137/1020043
6. M. Golubitsky and B. Keyfitz, A qualitative study of the steady-state solutions for a continuous flow stirred tank chemical reactor, SIAM J. Appl. Math. (submitted).
M. Golubitsky and D. Schaeffer, A theory for imperfect bifurcation via singularity theory, Comm. Pure Appl. Math. 32 (1979), no. 1, 21–98. MR 508917, DOI 10.1002/cpa.3160320103
M. Golubitsky and D. Schaeffer, Imperfect bifurcation in the presence of symmetry, Comm. Math. Phys. 67 (1979), no. 3, 205–232. MR 539727
Valentin Poénaru, Singularités $C^{\infty }$ en présence de symétrie, Lecture Notes in Mathematics, Vol. 510, Springer-Verlag, Berlin-New York, 1976. En particulier en présence de la symétrie d’un groupe de Lie compact. MR 0440597
David G. Schaeffer and Martin A. Golubitsky, Bifurcation analysis near a double eigenvalue of a model chemical reaction, Arch. Rational Mech. Anal. 75 (1980/81), no. 4, 315–347. MR 607902, DOI 10.1007/BF00256382
11. D. Schaeffer and M. Golubitsky, Boundary conditions and mode jumping in the buckling of a rectangular plate, Comm. Pure Appl. Math. (submitted).
12. S. Smale, Review of Catastrophe theory, Selected Papers, 1972-1977 by E. C. Zeeman, Bull. Amer. Math. Soc. 84 (1978), 1360-1367.
13. I. N. Stewart, The seven elementary catastrophes, The New Scientist, Nov. 20, 1975, 447-454.
Héctor J. Sussmann, Catastrophe theory, Synthese 31 (1975), no. 2, 229–270. Mathematical methods of the social sciences. MR 474381, DOI 10.1007/BF00485979
Héctor J. Sussmann and Raphael S. Zahler, Catastrophe theory as applied to the social and biological sciences: a critique, Synthese 37 (1978), no. 2, 117–216. Mathematical methods in the social sciences, III. MR 495176, DOI 10.1007/BF00869575
Floris Takens, Singularities of vector fields, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 47–100. MR 339292
René Thom, Stabilité structurelle et morphogénèse, Mathematical Physics Monograph Series, W. A. Benjamin, Inc., Reading, Mass., 1972 (French). Essai d’une théorie générale des modèles. MR 0488155
J. M. T. Thompson and G. W. Hunt, A general theory of elastic stability, Wiley-Interscience [John Wiley & Sons], London-New York-Sydney, 1973. MR 0400868
John M. T. Thompson and Giles W. Hunt, Towards a unified bifurcation theory, Z. Angew. Math. Phys. 26 (1975), no. 5, 581–603 (English, with German summary). MR 388441, DOI 10.1007/BF01594031
20. E. C. Zeeman, Catastrophe theory, Sci. Amer. 234 (1976), 65-83.
E. C. Zeeman, Catastrophe theory, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1977. Selected papers, 1972–1977. MR 0474383
- 1.
- V. I. Arnold, Lectures on bifurcations in versal families, Russian Math. Surveys 27 (1975), 54-123. MR 0801647
- 2.
- M. V. Berry and M. R. Mackley, The six roll mill: unfolding an unstable persistently extensional flow, Philos. Trans. Roy. Soc. London Ser. A 287 (1977), 1-16. MR 489464
- 3.
- D. Chillingworth, Elementary catastrophe theory, Bull. Inst. Math. Appl. 11 (1975), 155-159. MR 494223
- 4.
- J. J. Callahan, Singularities and plane maps, Amer. Math. Monthly 81 (1974), 211-240. MR 353336
- 5.
- M. Golubitsky, An introduction to catastrophe theory and its applications, SIAM Rev. 20 (1978), 352-387. MR 470984
- 6.
- M. Golubitsky and B. Keyfitz, A qualitative study of the steady-state solutions for a continuous flow stirred tank chemical reactor, SIAM J. Appl. Math. (submitted).
- 7.
- M. Golubitsky and D. Schaeffer, A theory for imperfect bifurcation theory via singularity theory, Comm. Pure Appl. Math. (to appear). MR 508917
- 8.
- M. Golubitsky and D. Schaeffer, Imperfect bifurcation in the presence of symmetry, Comm. Math. Phys. (to appear). MR 539727
- 9.
- V. Poénaru, Singularities C, Lecture Notes in Math., vol. 510, Springer-Verlag, New York, 1976. MR 440597
- 10.
- D. Schaeffer and M. Golubitsky, Bifurcation analysis near a double eigenvalue of a model chemical reaction, Arch. Rational Mech. Anal. (to appear). MR 607902
- 11.
- D. Schaeffer and M. Golubitsky, Boundary conditions and mode jumping in the buckling of a rectangular plate, Comm. Pure Appl. Math. (submitted).
- 12.
- S. Smale, Review of Catastrophe theory, Selected Papers, 1972-1977 by E. C. Zeeman, Bull. Amer. Math. Soc. 84 (1978), 1360-1367.
- 13.
- I. N. Stewart, The seven elementary catastrophes, The New Scientist, Nov. 20, 1975, 447-454.
- 14.
- H. J. Sussmann, Catastrophe theory, Synthèse 31 (1975), 229-270. MR 474381
- 15.
- H. J. Sussmann and R. S. Zahler, Catastrophe theory as applied to the social and biological sciences: a critique, Synthèse 37 (1978), 117-216. MR 495176
- 16.
- F. Takens, Singularities of vector fields, Inst. Hautes Étude Sci. Publ. Math. 43 (1973), 47-100. MR 339292
- 17.
- R. Thom, Stabilité structurelle et morphogénèse, Benjamin, Reading, Mass., 1972; English transl, (by D. Fowler), 1975. MR 488155
- 18.
- J. M. T. Thompson and G. W. Hunt, A general theory of elastic stability, Wiley, London, 1973. MR 400868
- 19.
- J. M. T. Thompson and G. W. Hunt, Towards a unified bifurcation theory, J. Appl. Math. Phys. 26 (1975), 581-603. MR 388441
- 20.
- E. C. Zeeman, Catastrophe theory, Sci. Amer. 234 (1976), 65-83.
- 21.
- E. C. Zeeman, Catastrophe theory, Selected papers, 1972-1977, Addison-Wesley, Reading, Mass., 1977 MR 474383
Review Information:
Reviewer:
Martin Golubitsky
Journal:
Bull. Amer. Math. Soc.
1 (1979), 524-532
DOI:
https://doi.org/10.1090/S0273-0979-1979-14605-6
