20.500.12556/DKUM-89364 Parameterized family of annular homeomorphisms with pseudo-circle attractors 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 a unique topological object, called the R.H. Bing's pseudo-circle, yet display an interesting boundary dynamics. Namely, in the constructed family of homeomorphisms the outer prime ends rotation number vary continuously with the parameter through the interval [0, 1/2]. This, in particular, answers a question from Boroński et al. (2020) [15]. Furthermore, these attractors preserve the induced Lebesgue measure from the circle and have strong measure-theoretic and statistical properties. 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 the pseudo-solenoids. For degree one circle maps, this implies that the generic inverse limit in this context is the pseudo-circle. Lebesgue measure circle maps pseudo-circle Brown-Barge-Martin embeddings strange attractors Lebesgueova mera krožni zemljevidi psevdokrog Brown-Barge-Martinove vgradnje čudni atraktorji true false true Angleški jezik Slovenski jezik Znanstveno delo 2024-07-05 04:11:55 2025-02-26 09:23:05 2025-02-27 03:11:28 0000-00-00 00:00:00 2024 0 0 str. 102-132 Letn. 407 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2023-11-17 2024-06-05 2024-06-21 517.987 200659459 10.1016/j.jde.2024.06.008 0022-0396 RAZ_Cinc_Jernej_2024.pdf RAZ_Cinc_Jernej_2024.pdf 1 CFF5CFA149983435C954550E1A3124ED 2f322c1fd92da915cc28ab140daa91f337ae2e87d5f11c0198c8d6b7a459626c d0cb357c-f41a-11ef-a5fa-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=188828 https://doi.org/10.1016/j.jde.2024.06.008 0 dc704824-f41a-11ef-a5fa-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=188829 Fakulteta za naravoslovje in matematiko 0 0 0