Inverse Limit and Lauwerier Attractor(Ⅰ)

GUO Feng; LI Deng-hui; XIE Jian-hua

doi:10.3879/j.issn.1000-0887.2014.02.009

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GUO Feng, LI Deng-hui, XIE Jian-hua. Inverse Limit and Lauwerier Attractor(Ⅰ)[J]. Applied Mathematics and Mechanics, 2014, 35(2): 212-218. doi: 10.3879/j.issn.1000-0887.2014.02.009

Citation:

GUO Feng, LI Deng-hui, XIE Jian-hua. Inverse Limit and Lauwerier Attractor(Ⅰ)[J]. Applied Mathematics and Mechanics, 2014, 35(2): 212-218. doi: 10.3879/j.issn.1000-0887.2014.02.009

Citation:

GUO Feng, LI Deng-hui, XIE Jian-hua. Inverse Limit and Lauwerier Attractor(Ⅰ)[J]. Applied Mathematics and Mechanics, 2014, 35(2): 212-218. doi: 10.3879/j.issn.1000-0887.2014.02.009

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Inverse Limit and Lauwerier Attractor(Ⅰ)

doi: 10.3879/j.issn.1000-0887.2014.02.009

School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China

Funds: The National Natural Science Foundation of China(11172246;11272268)

Received Date: 2013-09-17
Rev Recd Date: 2013-12-05
Publish Date: 2014-02-15

Abstract

Abstract

A two dimensional Lauwerier mapping was studied and an analytical expression of the strange attractor was obtained. The dynamic properties of the shift map on the inverse limit space of the quadratic mapping were investigated. The projection mapping was established. Then the Lauwerier mapping was studied based on the theory of inverse limit space. It is proved that the Lauwerier mapping restricted to its attractor is topologically semi-conjugate to the shift map on the inverse limit space of the quadratic mapping; therefore the Lauwerier strange attractor is chaotic in the sense of Devaney.
- lauwerier mapping,
- unstable manifold,
- strange attractor,
- inverse limit space,
- shift map

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References(16)

References

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