Inverse problem in chaotic map theory

Inverse problem in chaotic map theory is formulated. Solvable chaotic maps having the given invariant measure ρ(x)=An/1-x2n of n=2n=2 and n=3n=3 are obtained. They are derived systematically by using multiplication formulas of the elliptic functions. The Lyapunov number λλ is also computed exactly for each map function, which is expressed commonly by λ=logmλ=logm in terms of the multiplication factor m.