## The Kolmogorov Legacy in PhysicsThe present volume, published at the occasion of his 100th birthday anniversary, is a collection of articles that reviews the impact of Kolomogorov's work in the physical sciences and provides an introduction to the modern developments that have been triggered in this way to encompass recent applications in biology, chemistry, information sciences and finance. This book addresses scientists and postgraduate students in applied mathematics and theoretical physics. |

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### Contents

Kolmogorov Pathways from Integrability to Chaos and Beyond | 3 |

From Regular to Chaotic Motions through the Work of Kolmogorov | 33 |

Dynamics at the Border of Chaos and Order | 61 |

Algorithmic Complexity and Information Theory | 83 |

Kolmogorovs Legacy about Entropy Chaos and Complexity | 85 |

Complexity and Intelligence | 109 |

Information Complexity and Biology | 123 |

Turbulence | 147 |

Fully Developed Turbulence | 149 |

Turbulence and Stochastic Processes | 173 |

Front Propagation and Spatial Structures | 187 |

Applications of Probability Theory | 211 |

From Kolmogorov to Renormalization Group | 213 |

From Batcheliers Random Walks to Multifractal Cascades | 229 |

### Common terms and phrases

A.N. Kolmogorov advection Aldo Moro Algorithmic Complexity anisotropic autocorrelation behavior bifurcation Biology cascade chaos chaotic dynamics characterized Chirikov consider correlation function corresponding defined depends deterministic diffusion dimensional discrete dissipation dynamical systems energy entropy equation estimate evolution example experimental exponential finite fluctuations fluid Fourier fractal frequency front Gaussian Hamiltonian systems information theory initial conditions integrable intermittency introduced invariant isotropic KAM theorem Kolmogorov complexity Kolmogorov-Sinai entropy length Lett limit linear Lyapunov exponents mathematical measure motion multifractal Navier-Stokes nonlinear obtained orbits parameter particle periodic perturbation phase space Phys physical prediction probability distribution problem propagation properties protein quantum quasi-periodic quasi-periodic motion random fields reaction renormalization resonance result Reynolds number scaling exponents Sect self-similar simulations small scale solution spatial spectrum stability Statistical Mechanics stochastic structure functions symbol theorem Thue-Morse sequence tion torus trajectories typical variables velocity differences velocity field volatility zero