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71.
We reconsider the continuity of the Lyapunov exponents for a class of smooth Schrödinger cocycles with a cos-type potential and a weak Liouville frequency. We propose a new method to prove that the Lyapunov exponent is continuous in energies. In particular, a large deviation theorem is not needed in the proof. 相似文献
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73.
Markus Kunze 《Journal of Dynamics and Differential Equations》2000,12(1):31-116
We consider dynamical systems from mechanics for which, due to some non-smooth friction effects, Oseledets' Multiplicative Ergodic Theorem cannot be applied canonically to define Lyapunov exponents. For general non-smooth systems which fit into a natural formal framework, we construct a suitable cocycle which lives on a good invariant set of full Lebesgue measure. Afterwards, this construction is applied to investigate a pendulum with dry friction, described through the equation
. The Lyapunov exponents obtained by our construction show a good agreement with the dynamical behaviour of the system, and since we will prove that these Lyapunov exponents are always non-positive, we conclude that the system does not show chaotic behaviour. 相似文献
74.
Bruce Ebanks 《Proceedings of the American Mathematical Society》2008,136(11):3911-3919
The main result is an improvement of previous results on the equation for a given function . We find its general solution assuming only continuous differentiability and local nonlinearity of . We also provide new results about the more general equation for a given function . Previous uniqueness results required strong regularity assumptions on a particular solution . Here we weaken the assumptions on considerably and find all solutions under slightly stronger regularity assumptions on .
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In this paper, we give the definition of the random periodic solutions of random dynamical systems. We prove the existence of such periodic solutions for a C1 perfect cocycle on a cylinder using a random invariant set, the Lyapunov exponents and the pullback of the cocycle. 相似文献
77.
This article establishes existence and uniqueness of solutions to two classes of stochastic systems with finite memory subject to anticipating initial conditions which are sufficiently smooth in the Malliavin sense. The two classes are semilinear stochastic functional differential equations (sfdes) and fully nonlinear sfdes with a sublinear drift term. For the semilinear case, we use Malliavin calculus techniques, existence of the stochastic semiflow and an infinite-dimensional substitution theorem. For the fully nonlinear case, we employ an anticipating version of the Itô–Ventzell formula due to Ocone and Pardoux [D. Ocone, E. Pardoux, A generalized Itô–Ventzell formula. Application to a class of anticipating stochastic differential equations, Annales de l’Institut Henri Poincaré. Probabilité s et Statistiques 25 (1) (1989) 39–71]. In both cases, the use of Malliavin calculus techniques is necessitated by the infinite dimensionality of the initial condition. 相似文献
78.
Friedrich Wagemann 《代数通讯》2013,41(5):1699-1722
Abstract The goal of this article is to construct a crossed module representing the cocycle 〈[,],〉 generating H 3(;?) for a simple complex Lie algebra . 相似文献
79.
Xiong Ping DAI 《数学学报(英文版)》2006,22(1):301-310
Let (X, G(X), m) be a probability space with a-algebra G(X) and probability measure m. The set V in G is called P-admissible, provided that for any positive integer n and positive-measure set Vn∈ contained in V, there exists a Zn∈G such that Zn belong to Vn and 0 〈 m(Zn) 〈 1/n. Let T be an ergodic automorphism of (X, G) preserving m, and A belong to the space of linear measurable symplectic cocycles 相似文献
80.
Sean McGuinness 《Journal of Graph Theory》2010,65(4):270-284
In this article, we show that for any simple, bridgeless graph G on n vertices, there is a family ?? of at most n?1 cycles which cover the edges of G at least twice. A similar, dual result is also proven for cocycles namely: for any loopless graph G on n vertices and ε edges having cogirth g*?3 and k(G) components, there is a family of at most ε?n+k(G) cocycles which cover the edges of G at least twice. © 2010 Wiley Periodicals, Inc. J Graph Theory 65: 270–284, 2010 相似文献