We consider both geometric and measure-theoretic shrinking targets for ergodic maps, investigating when they are visible or invisible. Some Baire category theorems are proved, and particular constructions are given when the underlying map is fixed. Open questions about shrinking targets are also described.
Rosenblatt, Joseph and Roychowdhury, Mrinal Kanti, "Geometric and Measure-Theoretic Shrinking Targets in Dynamical Systems" (2020). Mathematical and Statistical Sciences Faculty Publications and Presentations. 69.
Journal of Mathematical Analysis and Applications