کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4613852 | 1339273 | 2017 | 12 صفحه PDF | دانلود رایگان |
Suppose that X is a dendrite and f:X→Xf:X→X is a sensitive continuous map. We show that (a) (X,f)(X,f) contains a bilaterally transitive subsystem with nonempty interior; (b) the system (X,f)(X,f) satisfies only one of the following two conditions: (b1) (X,f)(X,f) contains a topologically transitive subsystem with nonempty interior; (b2) there exists an f-invariant nowhere dense closed subset A of X such that the attraction basin Basin(A,f)Basin(A,f) contains a residual subset B of an open set and the strong attraction basin Sbasin(A,f)Sbasin(A,f) is dense in B; (c) if X is completely regular, then (X,f)(X,f) contains a relatively strongly mixing subsystem with nonempty interior, dense periodic points and positive topological entropy. Unlike for interval maps, we construct a sensitive dendrite map with zero topological entropy.
Journal: Journal of Mathematical Analysis and Applications - Volume 446, Issue 1, 1 February 2017, Pages 908–919