Shadowing and expansivity in subspaces
Tom 219 / 2012
Fundamenta Mathematicae 219 (2012), 223-243 MSC: 37B45, 37E05, 54F15, 54H20. DOI: 10.4064/fm219-3-2
We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.