Title
Lyapunov exponent, Liao perturbation and persistence
Document Type
Article
Publication Date
9-1-2020
Abstract
© 2020, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature. 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.
Recommended Citation
Sun, Wenxiang and Young, Todd, "Lyapunov exponent, Liao perturbation and persistence" (2020). Mathematics Open Access Publications. 24.
https://ohioopen.library.ohio.edu/math-oapub/24