2023/05/10 by Jernej Činč, Piotr Oprocha, Činč, Jernej +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #37B45 #37C15 #37C20 #37E30 #37E45 #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #Primary 37E10 #Secondary 37A10
paper · pdf · doi:10.48550/arxiv.2305.06467
openalex publication_date 2023/05/10 · openalex created_date 2023/05/13 · openalex updated_date 2026/07/28
In this paper we construct a paramaterized family of annular homeomorphisms with Birkhoff-like rotational attractors that vary continuously with the parameter, are all homeomorphic to the pseudo-circle, display interesting boundary dynamics and furthermore preserve the induced Lebesgue measure from the circle. Namely, in the constructed family of attractors the outer prime ends rotation number vary continuously with the parameter through the interval [0,1/2]. This, in particular, answers a question from [J. London Math. Soc. (2) \bf 102 (2020), 557--579]. To show main results of the paper we first prove a result of an independent interest, that Lebesgue-measure preserving circle maps generically satisfy the crookedness condition which implies that generically the inverse limits of Lebesgue measure-preserving circle maps are hereditarily indecomposable. For degree one circle maps, this implies that the generic inverse limit in this context is the R.H. Bing's pseudo-circle.