Romero Ruiz del Portal, Francisco2023-06-202023-06-202004K. Borsuk, Theory of Shape, in: Monografie Mat., vol. 59,PWN, Warsaw, 1975. K. Borsuk, Theory of Retracts, in: Monografie Mat., vol.44, PWN, Warsaw, 1967. R.F. Brown, The Lefschetz Fixed Point Theorem, Scott Foreman, Glenview, IL, 1971. P. Le Calvez, J.C. Yoccoz, Un théoréme d’indice pour les homéomorphismes du plan au voisinage d’un point fixe, Ann. of Math. 146 (1997) 241–293. C.O. Christenson, W.L. Voxman, Aspects of Topology, BCS Associates, Moscow, ID, 1998. A. Dold, Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology 4 (1965)1–8. J. Franks, The Conley index and non-existence of minimal homeomorphisms, Illinois J. Math. 43 (3) (1999)457–464. J. Franks, D. Richeson, Shift equivalence and the Conley index, Trans. Amer. Math. Soc. 352 (7) (2000)3305–3322. M. Gidea, Leray functor and orbital Conley index for non-invariant sets, Discrete Continuous Dynamical Systems 5 (1999) 617–630. M. Gidea, The Conley index and countable decompositions of invariant sets, in: Conley Index Theory, in:Banach Center Publ., vol. 47, Polish Academy of Sciences, Warsaw, 1999, pp. 91–108. B. Kerékjártó, Voresungen über Topologie (I), Springer,Berlin, 1923. M. Mrozek, Index pairs and the fixed point index for semidynamical systems with discrete time, Fund.Math. 133 (1989). M. Mrozek, Leray functor and cohomological Conley index for discrete dynamical systems, Trans. Amer.Math. Soc. 318 (1990) 149–178. M. Mrozek, Shape index and other indices of Conley type for local maps on locally compact Hausdorff spaces, Fund. Math. 145 (1994). M. Mrozek, K.P. Rybakowski, A cohomological Conley index for maps on metrics spaces, J. Differential Equations 90 (1991) 143–171. R.D. Nussbaum, The fixed point index and some applications, in: Séminaire de Mathématiques Supérieures,Les Presses de L’Université de Montréal, 1985. J.W. Robbin, D. Salamon, Dynamical systems, shape theory and the Conley index, Ergodic Theory Dynamical Systems 8 (1988) 375–393. 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. F.R. Ruiz del Portal, J.M. Salazar, Shape index in metric spaces, Fund. Math. 176 (2003) 47–62. F.R. Ruiz del Portal, J.M. Salazar, A stable/unstable manifold theorem for local homeomorphisms of the plane,Ergodic Theory and Dynamical Systems, submitted for publication. A. Szymczak, The Conley index for discrete semidynamical systems, Topology Appl. 66 (3) (1995) 215–240. A. Szymczak, The Conley index for decompositions of isolated invariant sets, Fund. Math. 133 (1995) 71–90. A. Szymczak, The Conley index and symbolic dynamics,Topology 35 (1996) 287–299. P. Zgliczynski, Fixed point index for iterations,topological horseshoe and chaos, Topological Methods Nonlinear Anal. 8 (1996) 169–177.0166-864110.1016/j.topol.2003.12.013https://hdl.handle.net/20.500.14352/50700The author proves that if f is an orientation reversing homeomorphism of the plane and p is an isolated and stable fixed point of f then the fixed point index of f at p is equal to 1 . In the orientation preserving case this result was obtained by E. N. Dancer and R. Ortega [J. Dynam. Differential Equations 6 (1994), no. 4, 631–637. The proof is based on the prime ends compactifications method and a fixed point result by K. M. Kuperberg [Proc. Amer. Math. Soc. 112 (1991), no. 1, 223–229.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0166864103003808http://www.sciencedirect.com/restricted access515.1Fixed point indexConley indexFiltration pairs.Topología1210 Topología