［Purposes］ In order to extend the result of smooth linearization to torus, and know the dependence of parameters under disturbance. ［Methods］ A complete metric space is constructed by classical methods, and a special norm is defined to achieve compressibility of mapping. ［Findings］ The H?lder linearization of expending map is realized on one-dimensional circle, and the condition that makes the conjugate mappings H?lder depend on parameters is given. ［Conclusions］ Generally speaking, the linearization result can be improved to H?lder, and the linearization of circular dynamic system is consistent with that of one-dimensional linear dynamic system.