论文标题
非统计有理图
Non-statistical rational maps
论文作者
论文摘要
我们表明，在学位的家族中，$ d \ geq 2 $理性地图的理性地图，严格的后验证后有限的地图包含一个（相对）的baire baire bemaps映射子集，表现出最大的非稳态行为：显示出$ f $的最大$ f $在这个通用子集中的阶段，几乎是empir的阶段，几乎是empure ser的序列。所有$ f $ invariant措施的集合。证明是基于横向参数，该论点使我们能够控制严格的后有限后有限理性地图的关键点轨道的行为，也可以在作者的博士学位论文中开发了一个新概念，我们称之为统计分叉。
We show that in the family of degree $d\geq 2$ rational maps of the Riemann sphere, the closure of strictly postcritically finite maps contains a (relatively) Baire generic subset of maps displaying maximal non-statistical behavior: for a map $f$ in this generic subset, the set of accumulation points of the sequence of empirical measures of almost every point in the phase space is the largest possible one that is, the set of all $f$-invariant measures. The proofs is based on a transversality argument which allows us to control the behavior of the orbits of critical points for maps close to strictly postcritically finite rational maps and also a new concept developed in the author's PhD thesis, that we call statistical bifurcation.
