{"status":"public","publication_status":"published","title":"An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds","date_published":"2015-03-01T00:00:00Z","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:52:44Z","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","publisher":"Juliusz Schauder Center for Nonlinear Studies","year":"2015","volume":45,"type":"journal_article","month":"03","_id":"1563","publication":"Topological Methods in Nonlinear Analysis","abstract":[{"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/}.","lang":"eng"}],"scopus_import":1,"quality_controlled":"1","date_updated":"2021-01-12T06:51:37Z","page":"273 - 286","department":[{"_id":"HeEd"}],"doi":"10.12775/TMNA.2015.014","issue":"1","intvolume":"        45","citation":{"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>.","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>","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.","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>.","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>","short":"G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286.","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."},"publist_id":"5608","author":[{"last_name":"Graff","full_name":"Graff, Grzegorz","first_name":"Grzegorz"},{"first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk"}]}