A New Family of Exceptional Rational Functions

For each odd prime power q, we construct an infinite sequence of rational functions f(X) in F_q(X), which is exceptional, means that for infinitely many n the map c-->f(c) induces a bijection P^1(F_{q^n}). Moreover, our indecomposable, it cannot be written as composition lower-degree F_q(X). In case q not 3, these are first known examples indecomposable exceptional over F_q have non-solvable monodromy groups and arbitrarily large degree. These also wildly ramified f(X), other than linear changes polynomials.