کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778059 | 1633060 | 2017 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Transitive and series transitive maps on Rd
ترجمه فارسی عنوان
نقشه های ترانزیتی و پیوسته سری در جاده
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
چکیده انگلیسی
Motivated by the behavior of topologically transitive homomorphisms of Polish abelian groups, we say a continuous map f:RdâRd is 'series transitive' if for any two nonempty open sets U,VâRd, there exist xâU and nâN such that âj=0nâ1fj(x)âV. We show that any map on a discrete and closed subset of Rd can be extended to a mixing map of Rd, and use this result to produce a mixing map f:RdâRd (for each dâN) which is also series transitive. We have examples to say that transitivity and series transitivity are independent properties for continuous self-maps of Rd. We also construct a chaotic map (i.e., a transitive map with a dense set of periodic points) f:RdâRd such that f is arbitrarily close to and asymptotic to the identity map. Finally, we make a few observations about topological transitivity of continuous homomorphisms of Polish abelian groups.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 219, 15 March 2017, Pages 29-42
Journal: Topology and its Applications - Volume 219, 15 March 2017, Pages 29-42
نویسندگان
T.K. Subrahmonian Moothathu,