Romero Ruiz del Portal, FranciscoGraff, GrzegorzNowak-Przygodzki, Piotr2023-06-202023-06-2020111040-729410.1007/s10884-011-9204-7https://hdl.handle.net/20.500.14352/42017Let f : U →R2 be a continuous map, where U is an open subset of R2. We consider a fixed point p of f which is neither a sink nor a source and such that p is an isolated invariant set. Under these assumption we prove, using Conley index methods and Nielsen theory, that the sequence of fixed point indices of iterations ind(fn, p) n=1 is periodic,bounded by 1, and has infinitely many non-positive terms, which is a generalization of Le Calvez and Yoccoz theorem [Annals of Math., 146 (1997), 241-293] onto the class of non-injective maps. We apply our result to study the dynamics of continuous maps on 2-dimensional sphere.engjournal articlehttp://www.springerlink.com/openurl.asp?genre=journalissn=1040-7294open access515.1Fixed point indexConley indexNielsen numberPeriodic pointsIterationsTopología1210 Topología