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.
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.
Accepted:
Published online:
Antônio Endler 1; Jason A.C. Gallas 1
@article{CRMATH_2006__342_9_681_0,
author = {Ant\^onio Endler and Jason A.C. Gallas},
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},
}
Antônio Endler; Jason A.C. Gallas. Mandelbrot-like sets in dynamical systems with no critical points. Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 681-684. doi : 10.1016/j.crma.2006.02.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.02.027/
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