Abstract
Consider a C1 vector field together with an ergodic invariant probability that has ℓ nonzero Lyapunov exponents. Using orthonormal moving frames along a generic orbit we construct a linear system of ℓ differential equations which is a linearized Liao standard system. We show that Lyapunov exponents of this linear system coincide with all the nonzero exponents of the given vector field with respect to the given ergodic probability. Moreover, we prove that these Lyapunov exponents have a persistence property meaning that a small perturbation to the linear system (Liao perturbation) preserves both the sign and the value of the nonzero Lyapunov exponents.
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Acknowledgements
The first author was supported by National Natural Science Foundation of China (Grant Nos. 11771026 and 11831001). The authors thank the referees for their constructive suggestions.
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Dedicated to the Memory of Professor Shantao Liao at the Centenary of His Birth
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Sun, W., Young, T. Lyapunov exponent, Liao perturbation and persistence. Sci. China Math. 63, 1913–1928 (2020). https://doi.org/10.1007/s11425-019-1660-5
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DOI: https://doi.org/10.1007/s11425-019-1660-5