Read Online or Download Contribution to the theory of Lyapunov exponents for linear systems of differential equations PDF
Similar mathematics books
Leopold vintage Library is overjoyed to post this vintage e-book as a part of our huge assortment. As a part of our on-going dedication to providing price to the reader, we've additionally supplied you with a hyperlink to an internet site, the place you'll obtain a electronic model of this paintings at no cost. the various books in our assortment were out of print for many years, and hence haven't been obtainable to most of the people.
- Learning from Computers: Mathematics Education and Technology
- Minimal Surfaces in R3
- Mathematics and general relativity: proceedings of the AMS-IMS-SIAM joint summer research conference held June 22-28, 1986 with support from the National Science Foundation
- Acourse of pure mathematics
- Abstract Regular Polytopes (Encyclopedia of Mathematics and its Applications 92)
- Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operators (Mathematical Notes)
Extra info for Contribution to the theory of Lyapunov exponents for linear systems of differential equations
K. P. Persidskii, "On the stabil~ty of motion in the first approximation," Mat. , 40, No. 3, 284-292 (1933). I. G. Petrovskii, Lectures on the Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow (]970). M. M. Postnikov, Lectures on Geometry. llnd Semester. Linear Algebra and Differential Geometry [in Russian], Nauka, Moscow (1979). I. N. Sergeev, "Exact upper bounds of mobility for the Lyapunov exponents of a system of differential equations and the behavior of exponents under perturbations that tend to zero at infinity," Differents.
1. The normal decomposition E(A) = Elg:~... @Ea, of the space of solutions of equation A ~ is integrally separated if and only if every equation B ~ (A) admits a normal orthogonalizable decomposition with the same characteristics. 2. Suppose all Lyapunov exponents of equation A ~ are distinct. 6). 6~ In the case n = 2 a stronger statement, which requires no constraints on the Lyapunov exponents, holds true. 3. Let A ~ [ (R 2). Then the diagonalizability of all equations equivalent to the existence of an integrally separated decomposition B ~ (A) is E(A) =L@N, d i m L = d i m N = 1.
Functionals A i and are residual. 10 ~ . of space ~ . Proof. The maximal (minimal) i-th exponent is upper Pick an arbitrary equation A ~ . (lower) semicontinuous at any point The upper semicontinuity of functional %max I at the point A is verified as follows. 1, for every ~ > 0 there is an ~ > 0 sup ~ (B)< ~ x (A) + 6. p(A,B)<~ But t h e n f o r e v e r y e q u a t i o n C from the r ~max (C) • of equation sup A ~ (B )NK ~ ~ , tA , ) + 6, _ ~m p(B,C)
Contribution to the theory of Lyapunov exponents for linear systems of differential equations by Sergeev