Generic family displaying robustly a fast growth of the number of periodic points

Pierre Berger CNRS, Institut Mathématique de Jussieu Paris Rive Gauche, Université Sorbonne, Paris, France

TBD mathscidoc:2203.43009

Acta Mathematica, 227, (2), 205-262, 2021.12
For any 2⩽r⩽∞,n⩾2, we prove the existence of an open set U of C^r‑self‑mappings of any n‑manifold so that a generic map f in U displays a fast growth of the number of periodic points: the number of its n‑periodic points grows as fast as asked. This complements the works of Martens–de Melo–van Strien, Kaloshin, Bonatti–Díaz–Fisher and Turaev, to give a full answer to questions asked by Smale in 1967, Bowen in 1978 and Arnold in 1989, for any manifold of any dimension and for any smoothness. Furthermore, for any 1⩽r<∞ and any k⩾0, we prove the existence of an open set \hat U of k-parameter families in U such that for a generic (f_p)^p ∈ \hat U, for every ∥p∥⩽1, the map f_p displays a fast growth of the number of periodic points. This gives a negative answer to a problem asked by Arnold in 1992 in the finitely smooth case.
No keywords uploaded!
[ Download ] [ 2022-03-10 11:42:22 uploaded by actaadmin ] [ 289 downloads ] [ 0 comments ]
@inproceedings{pierre2021generic,
  title={Generic family displaying robustly a fast growth of the number of periodic points},
  author={Pierre Berger},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220310114222990694926},
  booktitle={Acta Mathematica},
  volume={227},
  number={2},
  pages={205-262},
  year={2021},
}
Pierre Berger. Generic family displaying robustly a fast growth of the number of periodic points. 2021. Vol. 227. In Acta Mathematica. pp.205-262. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220310114222990694926.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved