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This randomized trial demonstrates approximating Lyapunov exponents with periodic measures in hyperbolic fields, indicating new insights into invariant measures.
In this paper, we prove that for every C¹ star vector field on three-dimensional manifolds, every ergodic hyperbolic invariant measure which is not supported on singularities can be approximated by periodic measures and that the Lyapunov exponents of the ergodic hyperbolic invariant measure can also be approximated by the Lyapunov exponents of those periodic measures.
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Lu et al. (2026) studied this question.
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