International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 4, Pages 803-808
Dynamical properties of maps derived from maps with strong negative Schwarzian derivative
Department of Mathematics, Loyola Campus, Concordia University, Montréal H4B 1R6, Canada
Received 13 February 1984
Copyright © 1984 Abraham Boyarsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 as a stable periodic point and at most one other stable periodic orbit in the interior of the domain.