Lyapunov exponent, Liao perturbation and persistence

Autor:	Wenxiang Sun, Todd Young
Rok vydání:	2020
Předmět:	Mathematics::Dynamical Systems Differential equation General Mathematics Mathematical analysis Linear system Perturbation (astronomy) Lyapunov exponent Standard system symbols.namesake symbols Ergodic theory Orthonormal basis Vector field Mathematics
Zdroj:	Science China Mathematics. 63:1913-1928
ISSN:	1869-1862 1674-7283
DOI:	10.1007/s11425-019-1660-5
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::005b6c7d544a7cd39cb21e845ad3adf5 https://doi.org/10.1007/s11425-019-1660-5 Zobrazit plný text záznamu Full text from SpringerLink