For C^{1+α} diffeomorphisms, every hyperbolic ergodic measure's full Lyapunov spectrum can be approximated by the Lyapunov spectrum of a hyperbolic periodic orbit.
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Lyapunov exponents of hyperbolic measures and hyperbolic periodic orbits
For C^{1+α} diffeomorphisms, every hyperbolic ergodic measure's full Lyapunov spectrum can be approximated by the Lyapunov spectrum of a hyperbolic periodic orbit.