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French astronomer Michel Henon suggested a simplified model for the dynamics of the Lorenz system. There, he chosed to study mapping rather than differential equations because maps are faster to simulate and their solutions can be followd more accurately and for a longer time. Our aim is limited to the discussion of stability of the Henon map and the relations between this map and the horseshoe map. S. Smale introduced a map, which is called horseshoe map, probably the first example of a chaotic map. This article shows a simple explanation of this map and is devoted to well-known examples of two-dimensional functions : the baker' function, horseshoe map and Henon map. Henon map may appear to be chaotic. We see that Henon map (a>0,b=-1) appears to be chaotic. And the case (a<0,b=-1) is also shown.
- 共立薬科大学の論文
- 2001-06-01
共立薬科大学 | 論文
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