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A degenerate singularity generating geometric Lorenz attractors

Published online by Cambridge University Press:  14 October 2010

Freddy Dumortier ,
Hiroshi Kokubu  and
Hiroe Oka
Freddy Dumortier
Affiliation:
Departement Wiskunde, Limburgs Universitair Centrum, Universitaire Campus, B-3590 Diepenbeek, Belgium
Hiroshi Kokubu
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-01, Japan
Hiroe Oka
Affiliation:
Department of Applied Mathematics and Informatics, Faculty of Science and Technology, Ryukoku University Seta, Otsu 520-21, Japan
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Abstract

A degenerate vector field singularity in R3 can generate a geometric Lorenz attractor in an arbitrarily small unfolding of it. This enables us to detect Lorenz-like chaos in some families of vector fields, merely by performing normal form calculations of order 3.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 5 , October 1995 , pp. 833 - 856
Copyright
Copyright © Cambridge University Press 1995

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