[Ensembles de Mandelbrot dans les systèmes dynamiques sans points critiques]
Nous rapportons la découverte d'une quantité infinie d'ensembles de Mandelbrot dans l'espace des paramètres réels de la application d'Hénon, un difféomorphisme à deux dimension qui ne suit pas les conditions de Cauchy–Riemann et qui ne possède pas de points critiques. Pour des applications pratiques, nous montrons qu'il est possible de stabiliser une quantité infinie de phases complexes en ajustant seulement des paramètres réels.
We report the discovery of an infinite quantity of Mandelbrot-like sets in the real parameter space of the Hénon map, a bidimensional diffeomorphism not obeying the Cauchy–Riemann conditions and having no critical points. For practical applications, this result shows to be possible to stabilize infinitely many complex phases by tuning real parameters only.
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@article{CRMATH_2006__342_9_681_0,
author = {Endler, Ant\^onio and Gallas, Jason A.C.},
title = {Mandelbrot-like sets in dynamical systems with no critical points},
journal = {Comptes Rendus. Math\'ematique},
pages = {681--684},
publisher = {Elsevier},
volume = {342},
number = {9},
year = {2006},
doi = {10.1016/j.crma.2006.02.027},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.02.027/}
}
TY - JOUR AU - Endler, Antônio AU - Gallas, Jason A.C. TI - Mandelbrot-like sets in dynamical systems with no critical points JO - Comptes Rendus. Mathématique PY - 2006 SP - 681 EP - 684 VL - 342 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.02.027/ DO - 10.1016/j.crma.2006.02.027 LA - en ID - CRMATH_2006__342_9_681_0 ER -
%0 Journal Article %A Endler, Antônio %A Gallas, Jason A.C. %T Mandelbrot-like sets in dynamical systems with no critical points %J Comptes Rendus. Mathématique %D 2006 %P 681-684 %V 342 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.02.027/ %R 10.1016/j.crma.2006.02.027 %G en %F CRMATH_2006__342_9_681_0
Endler, Antônio; Gallas, Jason A.C. Mandelbrot-like sets in dynamical systems with no critical points. Comptes Rendus. Mathématique, Tome 342 (2006) no. 9, pp. 681-684. doi : 10.1016/j.crma.2006.02.027. http://www.numdam.org/articles/10.1016/j.crma.2006.02.027/
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