  We give effective bounds for the set quasi-integral points in orbits of
non-isotrivial rational maps over function fields under some conditions,
generalizing previous work of Hsia and Silverman (2011) for orbits over
function fields of characteristic zero. We then use this to prove finiteness
results for algebraic functions whose orbit under a rational function has
multiplicative dependent elements modulo rings of $S$-integers, generalizing
recent results over number fields.

Number Theory;Dynamical Systems