Sparsity of Iterations of Rational Functions on the Unit Circle

Key Points

• This research aims to establish a bound on how often polynomial iterations' orbit elements appear on the unit circle.
• Utilized results from Orevkov and Pakovich about lemniscate intersections of rational functions.
• Analyzed the behavior of polynomial iterations in relation to the unit circle.
• Defined a specific bound on the frequency of orbit elements landing on the unit circle.