Recently I have been reading the book Mathematical Tools for One-Dimensional Dynamics.
In the proof of the theorem 5.4.2, authors use the following fact that the number of attracting periodic points of a holomorphic family of rational maps is lower semicontinuous. However, there is no reference to that fact throughout the book elsewhere. Could it be possible to direct me to the proof of this fact.
I am new to the site and therefore would appreciate any comment you might have on improving the quality of my question (Also, I wasn't quite sure to ask the question here or on math.StackExchange).