A [111]-oriented Pt field emitter tip is used to study bistability and oscillations of CO oxidation by field electron microscopy (FEM) under low-pressure conditions (p(O2) = 4 x 10(-4) Torr, p(CO) = 8 x 10(-8) to 4 x 10(-5) Torr) in the temperature range 240 to 450 K. A kinetic phase diagram can be established, obtained on an FEM level with approximate to 2 nm lateral resolution. Below T approximate to 300 K a region of bistability prevails, and above T approximate to 300 K an oscillatory regime is obtained, thus yielding a cross-shaped phase diagram. These phenomena are surface plane specific and visible at the {011} planes of Pt and their surroundings.