论文标题
具有嵌套不变锥结构及其应用的非自主系统的动力学
Dynamics of non-autonomous systems with nested invariant cone structure and its applications
论文作者
论文摘要
在非自治（时间几乎是周期性的）情况下，目前的论文致力于研究嵌套不变锥结构对动力学的影响。我们首先证明在C1扰动下可以持续嵌套的不变锥结构。并且任何前轨道轨道的欧米茄限制组集合的动力学可以降低为合适的有限尺寸系统的紧凑型不变性的动力学（请参见定理2.1）。在某些特殊情况下，这种系统的偏斜产品半节产生的任何欧米茄限制设置的动力学类似于一个维度系统，即，欧米茄限制集合在大多数两个集合中都包含最小的集合，并且任何最小的集合都是由其基础流动的均等（几乎是自动化的），这是一个跨度的blober in S. the Universal-efriven se S. se Multivient se S. Multivientive niver-friven se S. se Multivientive driviven s.对于C1小扰动下的此类系统（请参见定理2.2，2.3）。据我们所知，这是第一篇文章触摸带有不变嵌套锥体抽象非自治系统的全球动态的论文。该设置是一般的，因为它包含一个自主系统加上几乎有周期性的扰动项，并且具有另一个周期性扰动项（这两个时期是非理性依赖）的周期系统。该结果可以看作是W. Shen和Y. Yi（1995 J.差异方程122 114-136）对具有分离边界条件的标态抛物线方程的重要作品的概括，Y. Wang（2007年非线性20 831-843）对于Tridiagonal竞争性合作系统（请参阅第4节）。
The current paper is devoted to the investigation of the influence of nested invariant cone structure on the dynamics, in the context of non-autonomous (time almost periodic)cases. We first prove that the nested invariant cone structure can persistent under C1 perturbations; and the dynamics of the omega-limit set of any precompact orbit can be reduced to the dynamics of a compact invariant of a suitable finite dimensional system(see Theorem 2.1). In some special cases, the dynamics of any omega-limit set generated by the skew product semiflow of such a system is similar to a one-dimensional system, that is, the omega-limit set contains at most two minimal sets, and any minimal set is an almost automorphic extension of its base flow(a universal phenomenon in multi-frequency driven systems, introduced by S. Bochner), these results are also correct for such systems under C1 small perturbations(see Theorems 2.2, 2.3). To our best knowledge, it is the first paper to touch the global dynamics of abstract non-autonomous systems with invariant nested cones; the setting is general, since it contains an autonomous system plus an almost-periodic perturbation term, and a periodic system with another periodic perturbation term (these two periods are irrationally dependent)as special cases. The results can be viewed as a generalization of important works of W. Shen and Y. Yi(1995 J. Differential Equations 122 114-136) for scalar parabolic equations with separated boundary conditions, Y. Wang(2007 Nonlinearity 20 831-843) for tridiagonal competitive cooperative systems(see Section 4).
