Once more on the Lefschetz fixed point theorem

• Autorzy: Górniewicz L. , Ślosarski M.
• Języki publikacji: EN

Abstrakty

EN

An abstract version of the Lefschetz fixed point theorem is presented. Then several generalizations of the classical Lefschetz fixed point theorem are obtained.

Słowa kluczowe

EN

Lefschetz number; fixed points; ANR; AR

PL

punkt stały

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 2
• Strony: 161--170
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Górniewicz L.

autor

Ślosarski M.

• Schauder Center for Nonlinear Studies, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland,

Bibliografia

• [1] J. Andres and L. Gorniewicz, Topological Principles for Boundary Value Problems, Kluwer, 2003.
• [2] K. Borsuk, Theory of Retracts, PWN, Warszawa 1966.
• [3] C. Bowszyc, Fixed point theorem for the pairs of spaces, Bull. Acad. Polon. Sci. 16 (1968), 845-851.
• [4] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott & Foresman, Glenview, IL, 1971.
• [5] G. Fournier, Generalisations du theoreme de Lefschetz pour des espaces noncompacts I-III; Bull. Acad. Polon Sci. 23 (1975), 693-699; 701-706; 707-711.
• [6] L. Gorniewicz, On the Lefschetz fixed point theorem, Math. Slovaca 52 (2002), 221-233.
• [7] —, On the Lefschetz fixed point theorem, in: Handbook of Topological Fixed Point Theory, Springer, 2005, 43-82.
• [8] A. Granas, Generalizing the Hopf-Lefschetz fixed point theorem for non-compac ANRs, in: Symposium on Infinite Dimensional Topology (Baton-Rouge, 1967), Ann. of Math. Stud. 69, Princeton Univ. Press, 1972, 119-130.
• [9] A. Granas and J. Dugundji, Fixed Point Theory, Springer, 2003.
• [10] W. Kryszewski, The Lefschetz type theorem for a class of noncompact mappings, Rend. Circ. Mat. Palermo (2) Suppl. 14 (1987), 365-384.
• [11] R. Nussbaum, Generalizing the fixed-point index, Math. Ann. 228 (1979), 259-278.
• [12] H. O. Peitgen, On the Lefschetz number for iterates of continuous mappings, Proc. Amer. Math. Soc. 54 (1976), 441-444. [
• [13] R. Srzednicki, A generalization of the Lefschetz fixed point theorem and detection of chaos, ibid. 128 (1999), 1231-1239.
• [14] R. B. Thompson, A unified approach to local and global fixed point indices, Adv. Math. 3 (1969), 1-71.