VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Parameterized family of annular homeomorphisms with pseudo-circle attractors
    Činč, Jernej ; Oprocha, Piotr
    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.
    Vir: Journal of differential equations. - ISSN 0022-0396 (Vol. 407, 2024, str. 102-132)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2024
    Jezik - angleški
    COBISS.SI-ID - 200659459

    Povezava(-e):

    Digitalna knjižnica Univerze v Mariboru – DKUM

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