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L'ordre dans le chaos : vers une approche déterministe de la turbulence / Pierre Bergé, Yves Pomeau, Christian Vidal ; préface de David Ruelle

Auteur principal : Bergé, Pierre, 1934-1997, AuteurCo-auteur : Vidal, Christian, 1942-, Auteur • Pomeau, Yves, 1942-, AuteurAuteur secondaire : Ruelle, David, 1935-, PréfacierType de document : MonographieCollection : Enseignement des sciences, 33Langue : français.Pays : France.Éditeur : Paris : Hermann, 1992Description : 1 vol. (XVI-353 p.) : ill. ; 24 cmISBN : 2705659803.ISSN : 0768-0341.Bibliographie : Bibliogr. Index.Sujet MSC : 37D45, Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior, Strange attractors, chaotic dynamics
37C55, Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory, Periodic and quasiperiodic flows and diffeomorphisms
37-01, Dynamical systems and ergodic theory, Instructional exposition (textbooks, tutorial papers, etc.)
76-02, Fluid mechanics, Research exposition (monographs, survey articles)
76Fxx, Fluid mechanics, Turbulence
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The book introduces the reader gradually to the field of chaos. The first two chapters present basic notions and results from oscillation theory. In Chapters III and IV are described two important methods of investigation of the behavior of a dynamical system: the Fourier transform and the Poincaré map. Three examples of dynamical systems are discussed in Chapter V: an electro-mechanical system with two degrees of freedom, the Rayleigh-Bérnard convection, and the Belousov-Zaboutinsky reaction. All these examples are also illustrated experimentally. The second part of the book deals with irregular, chaotic motion. The emphasis is put on the presentation of strange attractors, their geometric and dynamical characterisation. A special attention is given to the Ruelle-Takens theory of turbulence. At the end of the book some appendices are inserted that present notions of local bifurcation, Lyapunov exponents, and synchronization of oscillators. (Zentralblatt)

Bibliogr. Index

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