This work focuses on the second type of generalized Feigenbaum＇s equation {φ（f（x））=f（f（φ（x）））,f（0）=1,0≤f（x）≤1,x∈{0,1},where φ（x） is C∞-increasing function on [0, 1] and satisfies that φ（0） =...This work focuses on the second type of generalized Feigenbaum＇s equation {φ（f（x））=f（f（φ（x）））,f（0）=1,0≤f（x）≤1,x∈{0,1},where φ（x） is C∞-increasing function on [0, 1] and satisfies that φ（0） = 0,0 〈 φ′（x） 〈 1 （x ∈ [0, 1]）. Using constructive method, we discuss the existence of C∞-single-valley solutions whose derivatives are not equal to 0 on origin of the above equation.展开更多
基金Supported by National Natural Science Foundation of China,Tian Yuan Foundation(Grant No.11326129)the Fundamental Research Funds for the Central Universities(Grant No.14CX02152A)
文摘This work focuses on the second type of generalized Feigenbaum＇s equation {φ（f（x））=f（f（φ（x）））,f（0）=1,0≤f（x）≤1,x∈{0,1},where φ（x） is C∞-increasing function on [0, 1] and satisfies that φ（0） = 0,0 〈 φ′（x） 〈 1 （x ∈ [0, 1]）. Using constructive method, we discuss the existence of C∞-single-valley solutions whose derivatives are not equal to 0 on origin of the above equation.
