切比雪夫映射族关联函数的指数型丢番图方程  

Exponential Diophantine equations for correlation functions of Tchebyscheff maps

作　　者：周兴旺[1] ZHOU Xing-Wang(School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2023年第6期66-71,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(12171335);桥梁无损检测与工程计算四川省高校重点实验室开放项目(2022QYJ07)。

摘　　要：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.Tchebyscheff map is a typical chaotic map and the correlation functions play a key role in the study of its 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 map.To solve the equation,we firstly reduce it to a new Diophantine equation with strictly increasing exponentials and nonzero coefficients.Then we introduce the definition of"block"and classify the reduced equations based on the number of blocks constructing the equation,thus transform the problem of solving the equation to solve the new equations constructed by blocks.Finally we solve the equations constructed by one block and two blocks and exemplify the application of the main results.

关 键 词：指数型丢番图方程 关联函数 切比雪夫映射 

分 类 号：O156.7[理学—数学]