Reversible maps and their symmetry lines

In this paper, we present some methods to determine whether a planar map is reversible. Using these methods, we show that four automorphisms are reversible including Cremona map, cubic Hénon map, Knuth map and McMillan map. Some of them are not polynomial automorphism. We give the recurrence formulas of their symmetry lines, draw their phase portraits and symmetry lines with MATLAB software. Some special properties of their symmetry lines are explained and their beauties are also visually displayed.