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arXiv · 1408.2119

Linéarisation d'une itération bornée dans Rd par des fonctions de Weierstrass

Guy Cirier
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Abstract

In this paper, we study an iteration in defined by a diffeomorphism polynomial bounded. Semi invariant curves tend to curves with parametric Weierstrass-Mandelbrot's functions. So, self-similarity and fractal dimension are justified. We apply these results to partial differential calculus. On étudie une itération de Rd dans Rd définie par un difféomorphisme polynomial borné. On montre que les courbes semi invariantes tendent asymptotiquement vers des courbes paramétrées par des fonctions de Weierstrass. Cela justifie les calculs d'échelle d'autosimilarité et de dimension fractale comme le pratiquent des praticiens à partir d'intuitions pertinentes sur des itérations chaotiques. On applique ces résultats au calcul différentiel.

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Guy Cirier. 2014-08-27. Linéarisation d'une itération bornée dans Rd par des fonctions de Weierstrass. https://arxiv.org/abs/1408.2119

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