TY - JOUR
T1 - Normal forms on contracting foliations
T2 - smoothness and homogeneous structure
AU - Kalinin, Boris
AU - Sadovskaya, Victoria
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s10711-016-0153-5
DO - 10.1007/s10711-016-0153-5
M3 - Article
AN - SCOPUS:84961616521
SN - 0046-5755
VL - 183
SP - 181
EP - 194
JO - Geometriae Dedicata
JF - Geometriae Dedicata
IS - 1
ER -