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首页> 外文期刊>Annales Henri Poincare >Localized Stable Manifolds for Whiskered Tori in Coupled Map Lattices with Decaying Interaction
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Localized Stable Manifolds for Whiskered Tori in Coupled Map Lattices with Decaying Interaction

机译：耦合衰变相互作用的图格晶须花托的局部稳定流形

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摘要

In this paper we consider lattice systems coupled by local interactions. We prove invariant manifold theorems for whiskered tori (we recall that whiskered tori are quasi-periodic solutions with exponentially contracting and expanding directions in the linearized system). The invariant manifolds we construct generalize the usual (strong) (un)stable manifolds and allow us to consider also non-resonant manifolds. We show that if the whiskered tori are localized near a collection of specific sites, then so are the invariant manifolds. We recall that the existence of localized whiskered tori has recently been proven for symplectic maps and flows in Fontich et al. (J Diff Equ, 2012), but our results do not need that the systems are symplectic. For simplicity we will present first the main results for maps, but we will show that the result for maps imply the results for flows. It is also true that the results for flows can be proved directly following the same ideas.
机译：在本文中，我们考虑由局部相互作用耦合的晶格系统。我们证明了晶须花托的不变流形定理（我们记得晶须花托是线性系统中具有指数收缩和扩张方向的准周期解）。我们构造的不变流形概括了通常的（强）（不稳定）流形，并允许我们也考虑非谐振流形。我们表明，如果晶须花托被定位在特定位置的集合附近，那么不变流形也是如此。我们回想起最近在Fontich等人的辛映射图和流动中已经证明了局部晶须花托的存在。 （J Diff Equ，2012年），但是我们的结果不需要系统是辛的。为简单起见，我们将首先介绍地图的主要结果，但我们将显示地图的结果暗示流量的结果。同样可以直接根据相同的思想证明流量的结果。

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