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• W4280585971 abstract "The main goal of this paper is to study topological and measure-theoretic properties of an intriguing family of strange planar attractors. Building toward these results, we first show that any generic Lebesgue measure-preserving map f generates the pseudo-arc as inverse limit with f as a single bonding map. These maps can be realized as attractors of disc homeomorphisms in such a way that the attractors vary continuously (in Hausdorff distance on the disc) with the change of bonding map as a parameter. Furthermore, for generic Lebesgue measure-preserving maps f the background Oxtoby-Ulam measures induced by Lebesgue measure for f on the interval are physical on the disc and in addition there is a dense set of maps f defining a unique physical measure. Moreover, the family of physical measures on the attractors varies continuously in the weak* topology; that is, the parametrized family is statistically stable. We also find an arc in the generic Lebesgue measure-preserving set of maps and construct a family of disk homeomorphisms parametrized by this arc which induces a continuously varying family of pseudo-arc attractors with prime ends rotation numbers varying continuously in [0,1/2] . It follows that there are uncountably many dynamically non-equivalent embeddings of the pseudo-arc in this family of attractors." @default.
• W4280585971 created "2022-05-22" @default.
• W4280585971 creator A5014773516 @default.
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• W4280585971 date "2022-05-12" @default.
• W4280585971 modified "2023-10-16" @default.
• W4280585971 title "Parametrized family of pseudo‐arc attractors: Physical measures and prime end rotations" @default.
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• W4280585971 doi "https://doi.org/10.1112/plms.12448" @default.
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