Dynamical properties of maps derived from maps with strong negative Schwarzian derivative

Abstract

A strong Schwarzian derivative is defined, and it is shown that the convolution of a function with a map from an interval into itself having negative strong Schwarzian derivative is a function with negative Schwarzian derivative. Such convolutions have 0 as a stable periodic point and at most one other stable periodic orbit in the interior of the domain.

Keywords

• dynamical systems
• limiting behaviour
• Schwarzian derivative
• convolution
• stable periodic orbit.