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arXiv · 2006.12662

Non-stationary normal forms for contracting extensions

Boris Kalinin
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Abstract

We present the theory of non-stationary normal forms for uniformly contracting smooth extensions with sufficiently narrow Mather spectrum. We give coherent proofs of existence, (non)uniqueness, and a description of the centralizer results. As a corollary, we obtain corresponding results for normal forms along an invariant contracting foliation. The main improvements over the previous results in the narrow spectrum setting include explicit description of non-uniqueness and obtaining results in any regularity above the precise critical level, which is especially useful for the centralizer. In addition to sub-resonance normal form, we also prove corresponding results for resonance normal form, which is new in the narrow spectrum setting.

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Boris Kalinin. 2020-06-22. Non-stationary normal forms for contracting extensions. https://arxiv.org/abs/2006.12662

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