The structure of the bounded trajectories set of a scalar convex differential equation
The structure of the bounded trajectories set of a scalar convex differential equation
复制标题
标量凸微分方程有界轨迹集的结构
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
R. Obaya
中科院分区：
文献类型：
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作者：
A. Alonso;R. Obaya
本文描述了由一个标量凸微分方程定义的流的有界轨线集的拓扑结构和遍历结构。我们刻画的最小子集，遍历措施集中在他们身上，并研究长期的行为的有界轨迹的线性化方程的李雅普诺夫指数。特别是，我们得到的条件，保证存在的几乎周期，几乎自守和经常性的解决方案。
The present paper describes the topological and ergodic structure of the set of bounded trajectories of the flow defined by a scalar convex differential equation. We characterize the minimal subsets, the ergodic measures concentrated on them, and study the longtime behaviour of the bounded trajectories in terms of the Lyapunov exponents of the linearized equations. In particular, we obtain conditions that guarantee the existence of almost-periodic, almost-automorphic and recurrent solutions.