Skip to main content
SpringerLink
Log in

Openness of the set of boundary preserving maps of an annulus with intermingled attracting basins

  • Published:
Journal of Fixed Point Theory and Applications Aims and scope Submit manuscript

Abstract.

We prove that the set of smooth maps of an annulus with two attracting sets, both having metrically dense attracting basins, is open in an appropriate function space. Thus a 1994 claim of I. Kan is justified.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Yuli S. Ilyashenko

  2. Steklov Mathematical Institute, Moscow State and Independent Universities, Moscow, Russia

    Yuli S. Ilyashenko

  3. Moscow State University, Moscow, Russia

    Victor A. Kleptsyn

  4. University of Rennes, Rennes, France

    Petr Saltykov

Authors
  1. Yuli S. Ilyashenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Victor A. Kleptsyn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Petr Saltykov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuli S. Ilyashenko.

Additional information

To V. I. Arnold for more than half-centennial anniversary of his creative work, which in fluenced so many mathematicians, including the authors of this paper

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ilyashenko, Y.S., Kleptsyn, V.A. & Saltykov, P. Openness of the set of boundary preserving maps of an annulus with intermingled attracting basins. J. fixed point theory appl. 3, 449–463 (2008). https://doi.org/10.1007/s11784-008-0088-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11784-008-0088-z

Mathematics Subject Classification (2000).

Keywords.

Search

Navigation