Advanced Search
Article Contents
Article Contents

Realizing arbitrary $d$-dimensional dynamics by renormalization of $C^d$-perturbations of identity

  • * Corresponding author: Maria Saprykina

    * Corresponding author: Maria Saprykina

B. Fayad was supported in part by Knut and Alice Wallenberg foundation, grant KAW 2016.0403, and by the ANR-15-CE40-0001. M.Saprykina was supported in part by the Swedish Research Council, VR 2015-04012

Abstract Full Text(HTML) Related Papers Cited by
  • Any $ C^d $ conservative map $ f $ of the $ d $-dimensional unit ball $ {\mathbb B}^d $, $ d\geq 2 $, can be realized by renormalized iteration of a $ C^d $ perturbation of identity: there exists a conservative diffeomorphism of $ {\mathbb B}^d $, arbitrarily close to identity in the $ C^d $ topology, that has a periodic disc on which the return dynamics after a $ C^d $ change of coordinates is exactly $ f $.

    Mathematics Subject Classification: Primary: 37C15.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] D. V. Anosov and A. B. Katok, New examples in smooth ergodic theory. Ergodic diffeomorphisms, rudy Moskov. Mat. Obsc. 23 (1970), 3–36.
    [2] P. Berger and D. Turaev, On Herman's positive entropy conjecture, Adv. Math., 349 (2019), 1234-1288.  doi: 10.1016/j.aim.2019.04.002.
    [3] S. Ferenczi, Systèmes de rang un gauche, Ann. Inst. H. Poincaré Probab. Statist., 21 (1985), 177-186. 
    [4] M. Herman, Some open problems in dynamical systems, Proceedings of the International Congress of Mathematicians, Vol. 2, Berlin, 1998, Doc. Math., 1998, Extra Vol. II, 797–808.
    [5] J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc., 120 (1965), 286-294.  doi: 10.1090/S0002-9947-1965-0182927-5.
    [6] S. NewhouseD. Ruelle and F. Takens, Occurrence of strange Axiom A attractors near quasiperiodic flows on $ {\mathbb T}^m$, $m\geq 3$, Comm. Math. Phys., 64 (1978/79), 35-40.  doi: 10.1007/BF01940759.
    [7] D. Ruelle and F. Takens, On the nature of turbulence,, Comm. Math. Phys., 20 (1971), 167-192.  doi: 10.1007/BF01646553.
    [8] D. Turaev, Maps close to identity and universal maps in the Newhouse domain, Comm. Math. Phys., 335 (2015), 1235-1277.  doi: 10.1007/s00220-015-2338-4.
  • 加载中

Article Metrics

HTML views(341) PDF downloads(180) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint