Linearization of hyperbolic finite-time processes

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:254

Article

Karrasch, Daniel

关键词: Finite-time dynamics;    Hyperbolicity;    Spectral theorem;    Robustness;    Linearization;    Stable manifold;    Nonautonomous differential equations;   

DOI  :  10.1016/j.jde.2012.08.040

来源: Elsevier

【 摘 要 】

We adapt the notion of processes to introduce an abstract framework for dynamics in finite time, i.e. on compact time-sets. For linear finite-time processes a notion of hyperbolicity namely exponential monotonicity dichotomy (EMD) is introduced, thereby generalizing and unifying several existing approaches. We present a spectral theory for linear processes in a coherent way, based only on a logarithmic difference quotient. In this abstract setting we introduce a new topology, prove robustness of EMD and provide exact perturbation bounds. We suggest a new, intrinsic approach for the investigation of linearizations of finite-time processes, including finite-time analogues of the local (un-)stable manifold theorem and theorem of linearized asymptotic stability. As an application, we discuss our results for ordinary differential equations on a compact time-interval. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free