A new analytical method for the linearization of dynamic equation on measure chains. (English) Zbl 1126.34030

Xia, Yonghui; Cao, Jinde; Han, Maoan

J. Differ. Equations 235, No. 2, 527-543 (2007).

The authors deal with dynamical systems on measure chains (time scales). Such systems (their definition is too complicated to be given here; see, for example, the book by M. Bohner and A. Peterson [Dynamic equations on time scales. An introduction with applications. Basel: Birkhäuser (2001; Zbl 0978.39001)] are generalizations of ordinary differential equations. In this paper, the authors introduce a new method for establishing topological equivalence on measure chains between a nonlinear system and its linear part.

Reviewer: Sergei Yu. Pilyugin (St. Petersburg)

MSC:

34C41	Equivalence and asymptotic equivalence of ordinary differential equations
39A12	Discrete version of topics in analysis

Keywords:

measure chains; exponential dichotomy; linearization

Citations:

Zbl 0978.39001

References:

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