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Part of the book series: Springer Series in Synergetics ((SSSYN,volume 12))

Abstract

The thinking possibility of ‘turbulent’ behavior in chemically reacting systems was first seen by Ruelle and Takens [1] and Nicolis and Prigogine [2]. A few years later, when the Lorenz equation [3] was beginning to be appreciated as a concrete chaos-producing 3-variable ordinary differential equation, similarly behaving abstract reaction systems (belonging actually to a somewhat different, easier to analyze, type of equations; Rössler [4]) were soon seen and followed by experimental demonstrations; see Hudson and Mankin [5] and Pacault et al. [6] for reviews.

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References

  1. D. Ruelle and F. Takens, Commun. Math. Phys. 20, 167 (1971)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. G. Nicolis and I. Prigogine, Proc. Nat. Acad. Sci. (USA) 68, 2102 (1971)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)

    Article  ADS  Google Scholar 

  4. O.E. Rössler, Z. Naturforsch. Teil A 31, 259 (1976)

    Google Scholar 

  5. J.L. Hudson and J.C. Mankin, J. Chem. Phys. 74, 6171 (1981)

    Article  ADS  Google Scholar 

  6. A. Pacault and C. Vidal, These Proceedings

    Google Scholar 

  7. A.T. Winfree, Science 181, 937 (1973)

    Article  ADS  Google Scholar 

  8. O.E. Rössler and C. Kahlert, Z. Naturforsch. Teil A 34, 565 (1979)

    ADS  Google Scholar 

  9. Y. Kuramoto and T. Yamada, Progr. Theor. Phys. 55, 679 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  10. J. Guckenheimer, On a codimension two bifurcation (preprint 1979 )

    Google Scholar 

  11. O.E. Rössler and H. Thomas, in preparation

    Google Scholar 

  12. I.C. Percival, Advan. Chem. Phys. 36, 1 (1977)

    Article  Google Scholar 

  13. O.E. Rössler, Springer Lect. Notes Biomath. 4, 399 (1974)

    Article  Google Scholar 

  14. H. Nagashima, J. Phys. Soc. Japan 49, 2427 (1980)

    Article  ADS  Google Scholar 

  15. R.J. Field, E. Körös, and R.M. Noyes, J. Amer. Chem. Soc. 94, 8649 (1972)

    Article  Google Scholar 

  16. C. Darwin, in: Life and Letters of Charles Darwin, F. Darwin Ed., vol. 3, 202 ( Murray, London 1887 )

    Google Scholar 

  17. M. Ross, Berkeley (quoted in Time Magazine, 24 Aug. 1981, p. 55)

    Google Scholar 

  18. O.E. Rössler, Z. Naturforsch. Teil B 26, 741 (1971)

    Google Scholar 

  19. K.D. Willamowski and O.E. Rössler, Z. Naturforsch. Teil A 35, 317 (1980)

    ADS  Google Scholar 

  20. C. Kahlert, 0.E. Rössler and A. Varma, in: Proc. Heidelberg Workshop Modelling Chemical Reaction Systems 1980 (Springer Series of Chemical Physics 1981)

    Google Scholar 

  21. J.E. Cohen, in: Proc. Science in the Service of Life, Vienna 1979, M. Marois Ed.

    Google Scholar 

  22. H. Flechtner, Fundamental Notions of Cybernetics (in German) (Wissenschaftliche 86 Verlagsgesellschaft, Stuttgart 1968)

    Google Scholar 

  23. O.E. Rössler, BioSystems 11, 193 (1979)

    Article  Google Scholar 

  24. L. Boltzmann, Sitz.-Ber. Akad. Wiss. Wien II 66, 275 (1872)

    Google Scholar 

  25. A.S. Eddington, The Nature of the Physical World (Cambridge University Press, Cambridge 1929)

    MATH  Google Scholar 

  26. I. Prigogine and I. Stengers, Dialogue with Nature (in German)(Piper, München 1981 )

    Google Scholar 

  27. E. Hopf, Ergodic Theory (in German) p. 42 ( Springer-Verlag, Berlin 1937)

    Google Scholar 

  28. Ya.G. Sinai, Sov. Math. Dokl. 4, 1818 (1963)

    MathSciNet  Google Scholar 

  29. J.P. Crutchfield and N.H. Packard, Symbolic dynamics of one dimensional maps (preprint 1981)

    Google Scholar 

  30. J. Hurley, Phys. Rev. A 23, 268 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  31. O.E. Rössler, in: New Approaches to Nonlinear Problems in Dynamics, P. Holmes Ed., 477 (SIAM, Philadelphia 1980 )

    Google Scholar 

  32. H. Minkowski, Space and Time (in German)(Teubner, Leipzig 1909 )

    Google Scholar 

  33. E. Husserl, On the Phenomenology of the Inner Consciousness of Time (in German), Collected Works = Husserliana, vol. 10 ( M. Nijhoff, The Hague 1966 )

    Google Scholar 

  34. K. Vonnegut, Slaughterhouse Five (Dell, New York 1968)

    Google Scholar 

  35. D.J. Todt, in: Kybernetik 68, H. Marco and G. Farber Eds., 465 ( Oldenbourg, Munich 1969 )

    Google Scholar 

  36. O.E. Rössler, in: Dynamics of Synergetic Systems, H. Haken Ed., 147 ( Springer-Verlag, Heidelberg 1980 )

    Google Scholar 

  37. A.K. Dewdney, J. Recreational Math. 12, 16 (1979)

    Google Scholar 

  38. L. Galgani, Statistical mechanics of weakly coupled oscillators presenting stochastic thresholds (preprint 1981)

    Google Scholar 

  39. R. Abraham and J.E. Marsden, Foundations of Mechanics, 2nd ed. (Freeman, San Francisco 1978)

    MATH  Google Scholar 

  40. J.L. Van Hemmen, Springer Lect. Notes Phys. 93, 232 (1979)

    Article  ADS  Google Scholar 

  41. R.P. Feynman, R.B. Leighton, and M. Sands, The Feynman Lectures on Physics, vol. 1 (Addison-Wesley, Reading, Mass. 1965)

    MATH  Google Scholar 

  42. A. Einstein, Ann. d. Phys. Ser. 4, 14, 354 (1904)

    Article  ADS  Google Scholar 

  43. A. Einstein, Ann. d. Phys. Ser. 4, 17, 132 (1905)

    Article  ADS  Google Scholar 

  44. M. Planck, Verh. d. D. Phys. Ges. 2, 237 (1900)

    Google Scholar 

  45. T.S. Kuhn, Black-body Theory and the Quantum Discontinuity 1894–1912 (Oxford University Press, New York 1978)

    Google Scholar 

  46. L. Boltzmann, Nature 51, 413 (1895)

    Article  ADS  Google Scholar 

  47. J.C. Maxwell, Theory-of Heat, p. 308 (1871)

    Google Scholar 

  48. D.F. Galouye, Simulachron-Two (Gregg, London 1964)

    Google Scholar 

  49. R. Descartes, Meditations on the First Philosophy (in Latin) (Soly, Paris 1641)

    Google Scholar 

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Rössler, O.E. (1981). Chaos and Chemistry. In: Vidal, C., Pacault, A. (eds) Nonlinear Phenomena in Chemical Dynamics. Springer Series in Synergetics, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81778-6_12

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  • DOI: https://doi.org/10.1007/978-3-642-81778-6_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-81780-9

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