具有稠密临界轨道和预不动临界轨道的单峰映射的丰富性

Abundance of Uenimodal Maps With Dense Critical Orbit and Prefixed Critical Orbit

证明了对于实二次族在参数空间存在正Ｌｅｂｅｓｇｕｅ测度集合Ｅ，使得Ｅ中几乎所有的参数，相应的映射在不变测度的支集上具有稠密的临界轨道；还证明了Ｅ中存在稠密集合使得相应映射的临界轨道进入它的反向不动点．

For the so-called quadratic family , it is proved that, there exists a positive Lebesgue mea- sure 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 all parameters in E; it is also proved that there is a dense set in K such that the critical orbit of the corresponding map enter the reversed fixed point.