There is a lot of random stuff around. For example
using OrdinaryDiffEqFunctionMap
function henon_map!(u_next, u, p, t)
u_next[1] = 1 + u[2] - 1.4 * u[1]^2
u_next[2] = 0.3 * u[1]
end
prob = DiscreteProblem(henon_map!, [0.5, 0.5], (0, 100))
sol = solve(prob, FunctionMap())
What exactly are you looking to do?