The Effect Of Derivative Product At Periodic Points On Chaotic Ergodic Properties Of A Function

Taking a function of one variable as an example, the relationship between its derivative at a periodic point and its chaotic ergodic property is studied. It is found and proved that if the absolute value of the product of N derivatives at N periodic point is less than 1, then the function cannot be ergodic chaotic. Then, this result is used for image encryption, which further confirms the main conclusion of the paper.