Abstract
For the so-called quadratic family, it is proved that, there exists a positive Lebesgue measure set E in the parameter space such that the corresponding map has a dense critical orbit in the support set of the invariant measure for almost all parameters in E; it is also proved that there is a dense set in E such that the critical orbit of the corresponding map enter the reversed fixed point.
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Foundation item: the National Natural Science Foundation of China (19501030)
Biography: Cao Yongluo (1967-)
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Yongluo, C., Lanyu, W. Abundance of unimodal maps with dense critical orbit and prefixed critica orbit. Appl Math Mech 21, 389–394 (2000). https://doi.org/10.1007/BF02463759
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DOI: https://doi.org/10.1007/BF02463759