## Chaos, Order, and PatternsThe 12 lectures from the first school of a new nonlinear program instituted by the NATO Scientific Affairs Division for graduate and professional physicists. They focus on the currently most active topics of nonlinear physics, such as spatio-temporal chaos, fluid turbulence, the description of stran |

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### Contents

Scaling Function Dynamics | 1 |

Renormalization Zygmund Smoothness and the Epstein Class | 25 |

Torus Maps | 35 |

Copyright | |

10 other sections not shown

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### Common terms and phrases

amplitude analysis approximation asymptotic attractor behavior bifurcation bifurcation diagram Bloch wall boundary Cantor set cells center manifold chaotic circle map complexity condition consider convection coordinate corresponding Coupled Map Lattices critical curve defined dendrite depends described diffeomorphism diffusion dimension dimensional domain dynamical systems Eckhaus eigenvalue equation example exists experimental Figure finite fixed point flow fluid fractal frequency front geometry global homoclinic infinite interval invariant isotropic iterate lattice Lett linear Lyapunov exponents mode mode-locking motion nonlinear obtained oscillators parameter partial mode-locking pattern periodic orbits perturbation phase space Phys physical Poincare section problem properties quasiperiodic ratio Rayleigh-Benard Convection region renormalization group resonance result rotation number s-waves saddle-node Saffman Taylor finger scaling function sequences spatial spectrum stable stationary solutions statistical structure Theorem theory thermodynamic topological torus trajectory transition turbulence unstable unstable manifolds variables vector velocity width zero