In this paper existence of local analytic solutions of a polynomial-like iterative func-tional equation is studied.As well as in previous work,we reduce this problem with the Schrder transformation to finding analyt...In this paper existence of local analytic solutions of a polynomial-like iterative func-tional equation is studied.As well as in previous work,we reduce this problem with the Schrder transformation to finding analytic solutions of a functional equation without iteration of the un-known function f.For technical reasons,in previous work the constant α given in the Schrder transformation,i.e.,the eigenvalue of the linearized f at its fixed point O,is required to fulfill that α is off the unit circle S1 or lies on the circle with the Diophantine condition.In this paper,we obtain results of analytic solutions in the case of α at resonance,i.e.,at a root of the unity and the case of α near resonance under the Brjuno condition.展开更多
基金Supported by the Foundation of Chongqing Municipal Education Commission(KJQN201800502,KJQN201900525)Foundation of youth talent of Chongqing Normal University(02030307-00039)Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0857)。
基金the Natural Science Foundation of Shandong Province (No.2006ZRB01066)
文摘In this paper existence of local analytic solutions of a polynomial-like iterative func-tional equation is studied.As well as in previous work,we reduce this problem with the Schrder transformation to finding analytic solutions of a functional equation without iteration of the un-known function f.For technical reasons,in previous work the constant α given in the Schrder transformation,i.e.,the eigenvalue of the linearized f at its fixed point O,is required to fulfill that α is off the unit circle S1 or lies on the circle with the Diophantine condition.In this paper,we obtain results of analytic solutions in the case of α at resonance,i.e.,at a root of the unity and the case of α near resonance under the Brjuno condition.
