奇次维保测度映象的紊动性态*
Chaotic Behavior of the Measure-Preserving Mappings with Odd Dimension
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摘要: 本文考察了一个三次保测度映象C,它亦是由Henon映象扩充而成的.我们研讨了它的紊动现象,并提供了由低维映象的紊动性来判定高维映象是否存在紊动性态的可能性.Abstract: In this paper, we consider the measure-preserving mapping C with dimension 3 which is also the expansion of Henon mapping. Then we study the character of its fixed points and chaotic behavior. Next we offer a possibility that using the chaotic behavior of the lower dimensional mappings brings about the higher.
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[1] Henon,M,,Numerical study of quadratic area-preserving mappings,Quart.Apll.Math27(1969),291. [2] 孙义隧,三维保测映象中的不变流形,Sci Sini.,27(1984),174. [3] Li,T,Y.,and J.A.Yorke,Period three implies chaos,Amer.Math.Monthlg,82(1975),985. -
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