Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Nielsen Type Numbers of Self-Maps on the Real Projective Plane | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 327493 9 pages doi 2010 327493 Research Article Nielsen Type Numbers of Self-Maps on the Real Projective Plane Jiaoyun Wang School of Mathematical Sciences and Institute of Mathematics and Interdisciplinary Science Capital Normal University Beijing 100048 China Correspondence should be addressed to Jiaoyun Wang wangjiaoyun@ Received 27 May 2010 Revised 26 July 2010 Accepted 23 September 2010 Academic Editor Robert F. Brown Copyright 2010 Jiaoyun Wang. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Employing the induced endomorphism of the fundamental group and using the homotopy classification of self-maps of real projective plane RP2 we compute completely two Nielsen type numbers NPn f and NF f which estimate the number of periodic points of f and the number of fixed points of the iterates of map f. 1. Introduction Topological fixed point theory deals with the estimation of the number of fixed points of maps. Readers are referred to 1 for a detailed treatment of this subject. The number of essential fixed point classes of self-maps f of a compact polyhedron is called the Nielsen number of f denoted N f . It is a lower bound for the number of fixed points of f. The Nielsen periodic point theory provides two homotopy invariants NPn f and NFn f called the prime and full Nielsen-Jiang periodic numbers respectively. A Nielsen type number NPn f was introduced in 1 which is a lower bound for the number of periodic points of least period n. Another Nielsen type number NF f can be found in 1 2 which is a lower bound for the number of fixed points of fn . The computation of these two Nielsen type numbers NPn f and NFn f is very difficult. There are very few results. Hart and Keppelmann calculated these two .
