---
_id: '1563'
abstract:
- lang: eng
  text: For a given self-map $f$ of $M$, a closed smooth connected and simply-connected
    manifold of dimension $m\geq 4$, we provide an algorithm for estimating the values
    of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic
    points in the smooth homotopy class of $f$. Our results are based on the combinatorial
    scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed
    Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm
    programmed in C++ is publicly available at {\tt http://www.pawelpilarczyk.com/combtop/}.
author:
- first_name: Grzegorz
  full_name: Graff, Grzegorz
  last_name: Graff
- first_name: Pawel
  full_name: Pilarczyk, Pawel
  id: 3768D56A-F248-11E8-B48F-1D18A9856A87
  last_name: Pilarczyk
citation:
  ama: Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number
    of periodic points for smooth self-maps of simply-connected manifolds. <i>Topological
    Methods in Nonlinear Analysis</i>. 2015;45(1):273-286. doi:<a href="https://doi.org/10.12775/TMNA.2015.014">10.12775/TMNA.2015.014</a>
  apa: Graff, G., &#38; Pilarczyk, P. (2015). An algorithmic approach to estimating
    the minimal number of periodic points for smooth self-maps of simply-connected
    manifolds. <i>Topological Methods in Nonlinear Analysis</i>. Juliusz Schauder
    Center for Nonlinear Studies. <a href="https://doi.org/10.12775/TMNA.2015.014">https://doi.org/10.12775/TMNA.2015.014</a>
  chicago: Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating
    the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected
    Manifolds.” <i>Topological Methods in Nonlinear Analysis</i>. Juliusz Schauder
    Center for Nonlinear Studies, 2015. <a href="https://doi.org/10.12775/TMNA.2015.014">https://doi.org/10.12775/TMNA.2015.014</a>.
  ieee: G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal
    number of periodic points for smooth self-maps of simply-connected manifolds,”
    <i>Topological Methods in Nonlinear Analysis</i>, vol. 45, no. 1. Juliusz Schauder
    Center for Nonlinear Studies, pp. 273–286, 2015.
  ista: Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal
    number of periodic points for smooth self-maps of simply-connected manifolds.
    Topological Methods in Nonlinear Analysis. 45(1), 273–286.
  mla: Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating
    the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected
    Manifolds.” <i>Topological Methods in Nonlinear Analysis</i>, vol. 45, no. 1,
    Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:<a href="https://doi.org/10.12775/TMNA.2015.014">10.12775/TMNA.2015.014</a>.
  short: G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015)
    273–286.
date_created: 2018-12-11T11:52:44Z
date_published: 2015-03-01T00:00:00Z
date_updated: 2021-01-12T06:51:37Z
day: '01'
department:
- _id: HeEd
doi: 10.12775/TMNA.2015.014
intvolume: '        45'
issue: '1'
language:
- iso: eng
month: '03'
oa_version: None
page: 273 - 286
publication: Topological Methods in Nonlinear Analysis
publication_status: published
publisher: Juliusz Schauder Center for Nonlinear Studies
publist_id: '5608'
quality_controlled: '1'
scopus_import: 1
status: public
title: An algorithmic approach to estimating the minimal number of periodic points
  for smooth self-maps of simply-connected manifolds
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2015'
...