Given any compact connected manifold M, we describe C2-open sets of iterated functions systems (IFS's) admitting fully-supported ergodic measures whose Lyapunov exponents along M are all zero. Moreover, these measures are approximated by measures supported on periodic orbits. We also describe C1-open sets of IFS's admitting ergodic measures of positive entropy whose Lyapunov exponents along M are all zero. The proofs involve the construction of non-hyperbolic measures for the induced IFS's on the flag manifold.
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