We study the Lipschitz metric on Outer Space and prove that fully irreducibleelements of Out(F_n) act by hyperbolic isometries with axes which are stronglycontracting. As a corollary, we prove that the axes of fully irreducibleautomorphisms in the Cayley graph of Out(F_n) are stable, meaning that aquasi-geodesic with endpoints on the axis stays within a bounded distance fromthe axis.
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