اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNonuniform dichotomy spectrum and reducibility for nonautonomous difference equations
91
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
For nonautonomous linear difference equations, we introduce the notion of the so-called nonuniform dichotomy spectrum and prove a spectral theorem. Moreover, we introduce the notion of weak kinematical similarity and prove a reducibility result by the spectral theorem.
قيم البحث
اقرأ أيضاً
We introduce new weak topologies and spaces of Caratheodory functions where the solutions of the ordinary differential equations depend continuously on the initial data and vector fields. The induced local skew-product flow is proved to be continuous
, and a notion of linearized skew-product flow is provided. Two applications are shown. First, the propagation of the exponential dichotomy over the trajectories of the linearized skew-product flow and the structure of the dichotomy or Sacker-Sell spectrum. Second, how particular bounded absorbing sets for the process defined by a Caratheodory vector field $f$ provide bounded pullback attractors for the processes with vector fields in the alpha-limit set, the omega-limit set or the whole hull of $f$. Conditions for the existence of a pullback or a global attractor for the skew-product semiflow, as well as application examples are also given.
This paper introduces a new difference scheme to the difference equations for N-body type problems. To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type difference eq
uations, the variational approach and the method of minimizing the Lagrangian action are adopted and the strong force condition is considered correspondingly, which is an efficient method in studying those with singular potentials. And the difference equation can also be taken into consideration of other periodic solutions with symmetric or choreographic constraint in further studies.
We give a sufficient condition for exponential stability of a network of lossless telegraphers equations, coupled by linear time-varying boundary conditions. The sufficient conditions is in terms of dissipativity of the couplings, which is natural fo
r instance in the context of microwave circuits. Exponential stability is with respect to any $L^p$-norm, $1leq pleqinfty$. This also yields a sufficient condition for exponential stability to a special class of linear time-varying difference delay systems which is quite explicit and tractable. One ingredient of the proof is that $L^p$ exponential stability for such difference delay systems is independent of $p$, thereby reproving in a simpler way some results from [3].
We consider general difference equations $u_{n+1} = F(u)_n$ for $n in mathbb{Z}$ on exponentially weighted $ell_2$ spaces of two-sided Hilbert space valued sequences $u$ and discuss initial value problems. As an application of the Hilbert space appro
ach, we characterize exponential stability of linear equations and prove a stable manifold theorem for causal nonlinear difference equations.
Coarse grained, macroscale, spatial discretisations of nonlinear nonautonomous partial differentialdifference equations are given novel support by centre manifold theory. Dividing the physical domain into overlapping macroscale elements empowers the
approach to resolve significant subgrid microscale structures and interactions between neighbouring elements. The crucial aspect of this approach is that centre manifold theory organises the resolution of the detailed subgrid microscale structure interacting via the nonlinear dynamics within and between neighbouring elements. The techniques and theory developed here may be applied to soundly discretise on a macroscale many dissipative nonautonomous partial differentialdifference equations, such as the forced Burgers equation, adopted here as an illustrative example.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
