四川大学学报（自然科学版）2023，Vol.60Issue(6)：66-71,6.DOI:10.19907/j.0490-6756.2023.061006
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
摘要
Abstract
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 equa-tion,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Key words
Exponential Diophantine equation/Correlation function/Tchebyscheff map分类
数理科学引用本文复制引用
周兴旺..切比雪夫映射族关联函数的指数型丢番图方程[J].四川大学学报（自然科学版）,2023,60(6):66-71,6.基金项目
国家自然科学基金(12171335) （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)) （2022QYJ07）
