The Lebesgue Measure of the Julia Sets of Permutable Transcendental Entire Functions  

作　　者：Cunji Yang Shaomin Wang Cunji Yang;Shaomin Wang(Department of Mathematics and Computer Science, Dali University, Dali, China)

机构地区：[1]Department of Mathematics and Computer Science, Dali University, Dali, China

出　　处：《Advances in Pure Mathematics》2022年第9期526-534,共9页理论数学进展（英文）

摘　　要：In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.

关 键 词：Transcendental Entire Function Permutable Functions Random Dynamics Julia Set Lebesgue Measure 

分 类 号：O15[理学—数学]