Normal forms on contracting foliations: smoothness and homogeneous structure

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In this paper we consider a diffeomorphism f of a compact manifold M which contracts an invariant foliation W with smooth leaves. If the differential of f on TW has narrow band spectrum, there exist coordinates Hx: Wx→ TxW in which f| W has polynomial form. We present a modified approach that allows us to construct maps Hx that depend smoothly on x along the leaves of W. Moreover, we show that on each leaf they give a coherent atlas with transition maps in a finite dimensional Lie group. Our results apply, in particular, to C1-small perturbations of algebraic systems.

Original languageEnglish (US)
Pages (from-to)181-194
Number of pages14
JournalGeometriae Dedicata
Issue number1
StatePublished - Aug 1 2016

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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