  In this paper, we manage to apply Schmidt games to certain non-algebraic
dynamical systems. More precisely, we show that the set of points with
non-dense forward orbit under a $C^2$-Anosov diffeomorphism with conformality
on unstable manifolds is a winning set for Schmidt games. It is also proved
that for a $C^{1+\theta}$-expanding endomorphism the set of points with
non-dense forward orbit is a winning set for certain variants of Schmidt games.
