论文标题
非均匀$μ$ - 二色谱谱和运动学相似性
Nonuniform $μ$-dichotomy spectrum and kinematic similarity
论文作者
论文摘要
对于线性非自主差分方程，我们引入了一个新的频谱系列，该频谱由一般不均匀的二分法定义：对于给定的大型增长率的给定增长率$μ$，我们考虑了一种频谱的概念，称为非均匀$ $ $ $ $ $ $ dichotomy spectrum。这个频谱家族包含非均匀的二分法谱系，是指数级生长速率的非常特殊的情况。对于每种增长率$μ$，我们描述了不均匀$ $ $ $二十莫的所有可能形式，将其连接的组件与适应的Lyapunov指数概念相关联，并使用它来获得非自主线性微分方程的可降低性结果。我们还提供了一个说明性的例子，其中获得了频谱，包括获得多项式行为正常形式的情况。
For linear nonautonomous differential equations we introduce a new family of spectrums defined with general nonuniform dichotomies: for a given growth rate $μ$ in a large family of growth rates, we consider a notion of spectrum, named nonuniform $μ$-dichotomy spectrum. This family of spectrums contain the nonuniform dichotomy spectrum as the very particular case of exponential growth rates. For each growth rate $μ$, we describe all possible forms of the nonuniform $μ$-dichotomy spectrum, relate its connected components with adapted notions of Lyapunov exponents, and use it to obtain a reducibility result for nonautonomous linear differential equations. We also give an illustrative examples where the spectrum is obtained, including a situation where a normal form is obtained for polynomial behavior.
