کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6418534 | 1339343 | 2014 | 14 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Length-expanding Lipschitz maps on totally regular continua Length-expanding Lipschitz maps on totally regular continua](/preview/png/6418534.png)
The tent map is an elementary example of an interval map possessing many interesting properties, such as dense periodicity, exactness, Lipschitzness and a kind of length-expansiveness. It is often used in constructions of dynamical systems on the interval/trees/graphs. The purpose of the present paper is to construct, on totally regular continua (i.e. on topologically rectifiable curves), maps sharing some typical properties with the tent map. These maps will be called length-expanding Lipschitz maps, briefly LEL maps. We show that every totally regular continuum endowed with a suitable metric admits a LEL map. As an application we obtain that every non-degenerate totally regular continuum admits an exactly Devaney chaotic map with finite entropy and the specification property.
Journal: Journal of Mathematical Analysis and Applications - Volume 412, Issue 1, 1 April 2014, Pages 15-28