Generalized theorem of Hartman-Grobman on measure chains

Journal of the Australian Mathematical Society

Stefan Hilger¹ 

关键词: 39A12;    34C20;   

DOI  :  10.1017/S1446788700037587

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We will prove the Theorem of Hartman-Grobman in a very general form. It states the topological equivalence of the flow of a nonlinear non-autonomous differential or difference equation with critical component to the flow of a partially linearized equation. The critical spectrum has not necessearily to be contained in the imaginary axis or the unit circle respectively. Further on we will employ the socalled calculus on measure chains within dynamical systems theory. Within this calculus the usual one dimensional time scales can be replaced by measure chains which are essentially closed subsets of R. The paper can be understood without knowledge of this calculus.So our main theorem will be valid even for equations defined on very strange time scales such as sequences of closed intervals. This is especially interesting for applications within the theory of differential-difference equations or within numerical analysis of qualitative phenomena of dynamical systems.

【 授权许可】

Unknown