  We show that a $C^1-$generic non partially hyperbolic symplectic
diffeomorphism $f$ has topological entropy equal to the supremum of the sum of
the positive Lyapunov exponents of its hyperbolic periodic points. Moreover, we
also prove that $f$ has topological entropy approximated by the topological
entropy of $f$ restrict to basic hyperbolic sets. In particular, the
topological entropy map is lower semicontinuous in a $C^1-$generic set of
symplectic diffeomorphisms far from partial hyperbolicity.
