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• W3183228678 abstract "The main goal of this paper is to study topological and measure-theoretic properties of an intriguing family of strange planar attractors. Building towards 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; i.e. 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 infinitely many dynamically non-equivalent embeddings of the pseudo-arc in this family of attractors." @default.
• W3183228678 created "2021-08-02" @default.
• W3183228678 creator A5014773516 @default.
• W3183228678 creator A5082078875 @default.
• W3183228678 date "2021-07-21" @default.
• W3183228678 modified "2023-09-27" @default.
• W3183228678 title "Pseudo-arc as the attractor in the disc -- topological and measure-theoretic aspects" @default.
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• W3183228678 hasPublicationYear "2021" @default.
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