Bifurcations of Equilibrium States

  • Vladimir Igorevich Arnold


An evolutionary process is described mathematically by a vector field in phase space. A point of phase space defines the state of the system. The vector at this point indicates the velocity of change of the state.


Phase Space Phase Curve Catastrophe Theory Node Saddle Degenerate System 
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Bibliographical Comments

Extensive bibliographies are contained in:

  1. T. Poston, I. Stewart: Catastrophe theory and its applications. Pitman, London-San Francisco-Melbourne 1978, 491 p.zbMATHGoogle Scholar
  2. V. I. Arnol’d, S. M. Gusein-Zade, A. N. Varchenko: Singularities of differentiable maps. vol. I, Nauka, Moscow 1982, 304 p. (English translation: Birkhäuser, Boston 1985, 382 p.) vol. II, Nauka, Moscow 1984, 336 p. (English translation: Birkhäuser, Boston, to appear)MathSciNetGoogle Scholar
  3. E. C. Zeeman, B. W. W.: 1981 Bibliography on catastrophe theory. Coventry, University of Warwick 1981, 73 p.Google Scholar
  4. V. I. Arnol’d: Singularities of systems of rays. Usp. Mat. Nauk 38:2 (1983), 77–147 (English translation: Russ. Math. Surv. 38:2 (1983), 87-176).Google Scholar
  5. Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. (Contemporary Problems of Mathematics) 22, Viniti, Moscow 1983 (English translation: J. Sov. Math. 27:3 (1984)).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Vladimir Igorevich Arnold
    • 1
  1. 1.Department of MathematicsUniversity of MoscowMoscowUSSR

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