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MODULI-FREE NORMAL FORMS AND LINEARIZATION OF VECTOR FIELDS

CHENGZHI LI

LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

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ZHIHUA REN

LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

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JIAZHONG YANG

LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

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https://doi.org/10.1142/S0218127406017154Cited by:2 (Source: Crossref)

Abstract

In this paper we study C¹ linearization and classification of germs of hyperbolic vector fields on Rⁿ. Two sets of algebraic conditions imposed on the eigenvalues of vector fields are given, under either of which strict similarity of the linear parts is necessary and sufficient for C¹ conjugacy of two vector fields. Furthermore, one set of the algebraic conditions together with strict similarity also imply linearization.

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