切比雪夫映射族关联函数的指数型丢番图方程

切比雪夫映射族是一类典型的混沌映射,关联函数是研究其统计性质的关键.本文所研究的指数型丢番图方程源于该映射族的关联函数的计算问题.为求得该方程的解,本文首先对该方程进行简化,使简化后的方程具有严格单调递增的指数及非零系数.然后本文引入了“块”的概念,根据简化方程所含块的个数对其进行了分类,进而将原丢番图方程求解问题转化为由块所构成的丢番图方程的求解问题.本文最后研究了一个和两个块的情形,并举例说明了本文结果的应用.

Exponential Diophantine equations for correlation functions of the Tchebyscheff maps

Tchebyscheff maps are typical chaotic maps. Correlation functions play a key role in the study of their statistical properties. This paper aims at the solutions of a class of exponential Diophantine equations arising in the calculation of correlation functions of the Tchebyscheff maps. To solve the equation, we firstly reduce it to a new equation with strictly increasing exponentials and nonzero coefficients. Then we introduce the definition of "block" and classify the reduced equations according to the number of blocks constructing the equation, thus transform the problem to solve the equations constructed by blocks. Finally we solve the equations constructed by only one block and two blocks and exemplify the application of main results.