Small C1-smooth perturbations of skew products and the partial integrability property

Abstract

In this paper we investigate stability of the integrability property of skew products of interval maps under small C1-smooth perturbations satisfying some conditions. We obtain here (sufficient) conditions of the partial integrability for maps under considerations. These conditions are formulated in the terms of properties of the unperturbed skew product. We give also the example of the partially integrable map.

Keywords

• skew products of interval maps
• perturbation
• integrability of a discrete dynamical system
• partial integrability of a discrete dynamical system
• curvelinear fiber
• 37exx
• 37cxx