## Dynamical Systems: A Renewal of Mechanism : Centennial of George David BirkhoffThis book commemorates the centenary of the birth of Georges David Birhoff, the father of the theory of Dynamical Systems. It consists of a volume of dedicated papers, reflecting the intellectual revolution of his work. This book is divided into four parts: Fundamental Paradigms — Chaos, Turbulence, Attractors, Bifurcations; Dynamical Systems and Microphysics; Self-Organization and Biological Dynamical Systems; Epistemology and History. |

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### Contents

where do we stand? | 13 |

WILLEMS Models for dynamical phenomena | 29 |

GUMOWSKI Recurrences and the transition from point to | 43 |

P BRUTER Bifurcation and continuity | 70 |

Z MARIC M BOZlC and D DAVIDOVIC Randomness and determinism in | 86 |

FARGUE Particles and classical1ike theories | 104 |

P B SCHEURER Time its structural coding and quantum kinetics | 123 |

VIDAL Spatial selforganization phenomena in chemical systems | 142 |

ZEEMAN Dynamics of Darwinian evolution | 155 |

DEMETRIUS Ergodic theory and dynamical systems in evolutionary | 166 |

G A CARPENTER Some cellbiological mechanisms governing complex | 180 |

J TONNELAT Normal tendency toward formation of singularities | 222 |

MIRA Some historical aspects concerning the theory of | 250 |

S DINER Epilogue | 273 |

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### Common terms and phrases

Andronov attractor behavior bifurcation biology Birkhoff Boltzmann bounce boundary completion Boundary Contour cells chaos concept considered Contour signals corresponds courbe defined definition described deterministic differential equations dynamical systems energy ensemble entropy equilibrium ergodic ergodic theory evolution example existence Feature Contour field Figure finite fixed point function G.D. Birkhoff geometric given global Grossberg Hamiltonian Hodgkin-Huxley model hypothesis implies interactions invariant irreversibility kinetic l'ensemble Leibniz linear Louis de Broglie Markovian markovian process mathematical measure motion mouvement récurrent mouvements limites nombre observed oméga orientation oscillations parameter particle periodic solution perturbation phase space phenomena Phys physical Poincare points-limites principle problem properties qualitative quantum mechanics receptive fields régions replication dynamic singular solution slow manifold solution segment species spikes stable statistical stochastic stochastic process structure theorem theory of dynamical thermodynamics tion tout transformation Turbulence upper sheet variables vector velocity wave