Lyapunov Exponents for Matrices with Invariant Subspaces
نویسندگان
چکیده
منابع مشابه
Asymptotic Lyapunov Exponents for Large Random Matrices
Suppose that A1, . . . , AN are independent random matrices whose atoms are iid copies of a random variable ξ of mean zero and variance one. It is known from the works of Newman et. al. in the late 80s that when ξ is gaussian then N−1 log ‖AN . . . A1‖ converges to a non-random limit. We extend this result to more general matrices with explicit rate of convergence. Our method relies on a simple...
متن کاملEla Invariant Neutral Subspaces for Hamiltonian Matrices
Hamiltonian matrices with respect to a nondegenerate skewsymmetric or skewhermitian indefinite inner product in finite dimensional real, complex, or quaternion vector spaces are studied. Subspaces that are simultaneously invariant for the matrices and neutral in the indefinite inner product are of special interest. The dimension of maximal (by inclusion) such subspaces is identified in terms of...
متن کاملInvariant neutral subspaces for Hamiltonian matrices
Hamiltonian matrices with respect to a nondegenerate skewsymmetric or skewhermitian indefinite inner product in finite dimensional real, complex, or quaternion vector spaces are studied. Subspaces that are simultaneously invariant for the matrices and neutral in the indefinite inner product are of special interest. The dimension of maximal (by inclusion) such subspaces is identified in terms of...
متن کاملEstimating Invariant Measures and Lyapunov Exponents
This paper describes a method for obtaining rigorous numerical bounds on time averages for a class of one-dimensional expanding maps. The idea is to directly estimate the absolutely continuous invariant measure for these maps, without computing trajectories. The main theoretical result is a bound on the convergence rate of the Frobenius-Perron operator for such maps. The method is applied to es...
متن کاملconstruction of vector fields with positive lyapunov exponents
in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1988
ISSN: 0091-1798
DOI: 10.1214/aop/1176991593