Strongly commuting interval maps
Tom 257 / 2022
Fundamenta Mathematicae 257 (2022), 39-68
MSC: 26A21, 37E05, 54H25, 54C10, 54C60.
DOI: 10.4064/fm993-11-2021
Opublikowany online: 3 December 2021
Streszczenie
Maps are called strongly commuting if f\circ g^{-1}=g^{-1}\circ f. We show that surjective, strongly commuting, strictly piecewise monotone maps f,g can be decomposed into a finite number of invariant intervals (or period 2 intervals) on which f,g are either both open maps, or at least one of them is monotone. As a consequence, two strongly commuting, strictly piecewise monotone interval maps have a common fixed point. Results of the paper also have implications in understanding dynamical properties of certain maps on inverse limit spaces.
