Liao Standard Systems and Nonzero Lyapunov Exponents for Differential Flows

Simple item page
dc.creatorSun, Wenxiang
dc.creatorYoung, Todd
dc.date2004-08-23
dc.date.accessioned2026-07-07T05:11:28Z
dc.date.available2026-07-07T05:11:28Z
dc.descriptionConsider a $C^1$ vector field together with an ergodic invariant probability that has $\ell$ nonzero Lyapunov exponents. Using orthonormal moving frames along certain transitive orbits we construct a linear system of $\ell$ differential equations which is a reduced form of Liao's "standard system". We show that the Lyapunov exponents of this linear system coincide with all the nonzero exponents of the given vector field with respect to the given probability. Moreover, we prove that these Lyapunov exponents have a persistence property that implies that a "Liao perturbation" preserves both sign and value of nonzero Lyapunov exponents.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/math/0408307
dc.identifierhttp://arxiv.org/abs/math/0408307
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72253
dc.subjectDynamical Systems
dc.subject37C15, 37A10, 34A26
dc.titleLiao Standard Systems and Nonzero Lyapunov Exponents for Differential Flows
dc.typetext

Files

Collections

arXiv