Journal of Dynamical and Control Systems

, Volume 22, Issue 3, pp 595–614 | Cite as

Sternberg Linearization Theorem for Skew Products

  • Yulij IlyashenkoEmail author
  • Olga Romaskevich


We present a special kind of normalization theorem: linearization theorem for skew products. The normal form is a skew product again, with the fiber maps linear. It appears that even in the smooth case, the conjugacy is only Hölder continuous with respect to the base. The normalization theorem mentioned above may be applied to perturbations of skew products and to the study of new persistent properties of attractors.


Normal forms Skew products Sternberg theorem 

Mathematics Subject Classification (2010)

37G05 37D30 



We are very thankful to Ilya Schurov and Stas Minkov for their attentive reading of the preliminary versions of this article and their remarks on the presentation. We are also grateful to the Referee for numerous valuable comments. Olga Romaskevich is mainly supported by UMPA ENS Lyon. (UMR 5669 CNRS) and the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR) as well as by the French-Russian Poncelet laboratory (UMI 2615 of CNRS and Independent University of Moscow). Both authors are supported by RFBR project 16-01-00748.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia
  2. 2.Cornell UniversityIthacaUSA
  3. 3.Independent University of MoscowMoscowRussia
  4. 4.École Normale Supérieure de LyonLyonFrance

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