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

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基金项目: 国家自然科学基金;(19501030)

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

摘要: 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。
- 单峰映射 /
- 二次族 /
- 不变测度
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.
- unimodal map /
- quadratic family /
- invariant measure

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