Recent results on iterative roots

Abstract

This is a rough survey of some results on iterative roots (fractional iterates) published recently. Also some historical information to clear the connection to previous results has been given. The main topics are: the conjugacy of piecewise monotonic functions and their iterative roots, stability of iterative roots, some substitutes and generalizations of the notion of iterative root using set-valued functions.

Keywords

• iteration
• iterative root
• topological conjugacy
• stability
• piecewise monotonic function
• set-valued function
• formal power series
• homeomorphism of the circle