Romero Ruiz del Portal, FranciscoSalazar, J. M.2023-06-202023-06-202010[1] I.K. Babenko, S.A. Bogatyi, The behavior if the index of periodic points under iterations of a mapping, Math. USSR Izvestiya, 38 (1992) 1-26. [2] C.Bonatti, J. Villadelprat, The index of stable critical points. Topology Appl. 126 (2002), 1-2, 263-271. [3] N.A. Bobylek, M.A.Krasnosels’kii, Deformation of a system into an asymptotically stable system, Automat remote control, 35 (1974) 1041-1044. [4] R.F. Brown, The Lefschetz fixed point theorem, Scott Foreman Co. Glenview Illinois, London (1971). [5] P.Le Calvez, J.C.Yoccoz, Un théoréme d’indice pour les homéomorphismes du plan au voisinage d’un poin fixe, Annals of Math. 146 (1997) 241-293. [6] P. Le Calvez, J.C. Yoccoz, Suite des indices de Lefschetz des itérés pour un domaine de Jordan qui est un bloc isolant, Unpublished. [7] P. Le Calvez, Dynamique des homéomorphismes du plan au voisinage d’un point fixe. Ann. Sci. Ecole Norm. Sup. (4) 36 (2003), no. 1, 139-171. [8] P. Le Calvez, F.R. Ruiz del Portal, J.M. Salazar, Fixed point indices of the iterates of R3-homeomorphisms at fixed points which are isolated invariant sets, J. London Math. Soc. (to appear). [9] S.N. Chow, J. Mallet-Paret, J.A. Yorke, A periodic orbit index which is a bifurcation invariant, Geometric Dynamics (Rio de Janeiro, 1981). Springer Lect. Notes in Mathematics, 1007. Berlin 1983, 109-131. [10] C. Christenson, W. Voxman, Aspects of topology, Marcel Dekker, Inc., New York and Basel, 1977. [11] E.N. Dancer, R. Ortega, The index or Lyapunov stable fixed points, Journal Dynamics and Diff. Equations, 6 (1994) 631-637. [12] A. Dold, Fixed point indices of iterated maps, Invent. Math., 74, (1983), 419-435. [13] E.Erle, Stable equilibria and vector field index, Topology Appl. 49 (1993) 231-235. [14] J.Franks, D.Richeson, Shift equivalence and the Conley index, Trans.Amer. Math. Soc. 352, 7 (2000) 3305-3322. [15] G.Graff, P.Nowak-Przygodzki, Fixed point indices of iterations of C1-maps in R3, Discrete and Continuous Dynamical Systems (to appear). [16] J. Jezierski, W. Marzantowicz, Homotopy Methods in Topological Fixed and Periodic Points Theory, Springer, 2005. [17] M.A.Krasnosel’skii, P.P.Zabreiko, Geometrical Methods of Nonlinear Analysis, Springer-Verlag, Berlin (1984). [18] R.D. Nussbaum, The fixed point index and some applications, Séminaire de Mathématiques supérieures, Les Presses de L’Université de Montréal, 1985. [19] F.R. Ruiz del Portal, Planar isolated and stable fixed points have index =1, Journal of Diff. Equations, 199 (2004), 179-188. [20] F.R. Ruiz del Portal, J.M. Salazar, Fixed point index of iterations of local homeomorphisms of the plane: a Conley-index approach, Topology 41 (2002) 1199-1212. [21] F.R. Ruiz del Portal, J.M. Salazar, A Poincaré formula for the fixed point indices of the iterations of arbitrary planar homeomorphisms, Fixed Point Theory Appl. (to appear). [22] F.R. Ruiz del Portal, J.M. Salazar, Indices of the iterates of R3-homeomorphisms at Lyapunov stable fixed points, Journal of Diff. Equations, 244 (2008) 1141-1156.0022-039610.1016/j.jde.2010.03.006https://hdl.handle.net/20.500.14352/42016The main goal of this paper is to prove that for each n > 2, every sequence of integers satisfying Dold’s congruences is realized as the sequence of fixed point indices of the iterates of an orientation preserving Rn-homeomorphism at an isolated stable fixed point. We use Conley index techniques even though stable fixed points are not isolated invariant sets.engjournal articlehttp://www.sciencedirect.com/science/journal/00220396open access515.1Conley indexFixed point indexStable fixed pointsHomeomorphismsTopología1210 Topología