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

Inverse Limit and Lauwerier Attractor(Ⅰ)

doi: 10.3879/j.issn.1000-0887.2014.02.009
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
  • 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.
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