An exotic Denjoy example of class
arXiv:2607.11616
summary
The paper constructs a C¹ diffeomorphism of the circle with an invariant Cantor minimal set whose gap lengths, when ordered decreasingly, have consecutive ratios that do not converge to 1, thereby answering a question of Dusa McDuff in the negative.
Abstract
We construct a -diffeomorphism of the circle having an invariant Cantor minimal set such that, when the lengths of the connected components of its complement are arranged in decreasing order, the ratios of consecutive lengths do not converge to 1. This gives a negative answer to a longstanding question posed by Dusa McDuff.
Topics & keywords
#circle diffeomorphisms#Denjoy example#invariant Cantor set#C¹ regularity#gap length ratiosC¹ diffeomorphismCantor minimal setDenjoy counterexamplegap length ratioMcDuff question