On the smoothness of conjugation of circle diffeomorphisms with rigid rotations

Abstract

We consider the operator which is a variable hysteron that describes, according to the Krasnosel'skii -Pokrovskii scheme, a nonstationary hysteresis nonlinearity with characteristics varying under external influences. We obtain sufficient conditions under which this operator is defined for inputs from the class of functions H¹[t₀, T] that satisfy the Lipschitz condition on the interval [t₀, T].