Abundance of unimodal maps with dense critical orbit and prefixed critica orbit

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. Foundation item: the National Natural Science Foundation of China (19501030) Biography: Cao Yongluo (1967-)