Schröder函数方程及其与混沌映射不变测度的关系
The Schröder functional equation and its relation to the invariant measures of chaotic maps
摘要：
证明了一类一维混沌映射的不变测度$T(x)$是由其导出的Schröder函数方程$q(T(x))=λq(x)$的推广解.因此，我们给出了一个统一的治疗，在目前的文献中制定的一系列精确解决的例子。特别是，我们表明，这些例子属于一类的功能介绍了米拉，（见文字）。此外，作为一个新的例子，我们计算了一类以Weierstrass $\wp$函数为不变函数的有理映射的不变密度.此外，我们还研究了该方程与著名的Frobenius-Perron算子和Koopman算子之间的关系。
英文摘要：
The aim of this paper is to show that the invariant measure for a class of one dimensional chaotic maps, $T(x)$, is an extended solution of the Schröder functional equation, $q(T(x))=λq(x)$, induced by them. Hence, we give an unified treatment of a collection of exactly solved examples worked out in the current literature. In particular, we show that these examples belongs to a class of functions introduced by Mira, (see text). Moreover, as a new example, we compute the invariant densities for a class of rational maps having the Weierstrass $\wp$ functions as an invariant one. Also, we study the relation between that equation and the well known Frobenius-Perron and Koopman's operators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
