کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4658051 1633077 2016 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Chain recurrent sets of generic mappings on compact spaces
ترجمه فارسی عنوان
مجموعه های مکرر زنجیره ای از نقشه های عمومی در فضاهای جمع و جور
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
چکیده انگلیسی

Let 0-CR denote the class of all metric compacta X   such that the set of maps f:X→Xf:X→X with 0-dimensional sets CR(f)CR(f) of chain recurrent points is a dense GδGδ-subset of the mapping space C(X,X)C(X,X) (with the uniform convergence). We prove, among others, that countable products of polyhedra or locally connected curves belong to 0-CR  . Compacta that admit, for each ϵ>0ϵ>0, an ϵ-retraction onto a subspace from 0-CR belong to 0-CR themselves. Perfect ANR-compacta or n  -dimensional LCn−1LCn−1-compacta have perfect CR(f)CR(f) for a generic self-map f. In the cases of polyhedra, compact Hilbert cube manifolds, local dendrites and their finite products, a generic f   has CR(f)CR(f) being a Cantor set and the set of periodic points of f   of arbitrarily large periods is dense in CR(f)CR(f). The results extend some known facts about CR(f)CR(f) of generic self-maps f on PL-manifolds.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 202, 1 April 2016, Pages 251–268
نویسندگان
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