Biblioteca de la Universidad Complutense de Madrid

A stable/unstable manifold theorem for local homeomorphisms of the plane


Romero Ruiz del Portal, Francisco y Salazar, J. M. (2005) A stable/unstable manifold theorem for local homeomorphisms of the plane. Ergodic Theory and Dynamical Systems, 25 (1). pp. 301-317. ISSN 1469-4417

[img] PDF

URL Oficial:


We use a notion (introduced in Topology 41 (2002), 1119–1212), which is stronger than the concept of filtration pair, to prove a stable/unstable manifold general theorem for local homeomorphisms of the plane in a neighborhood of an isolated fixed.

Tipo de documento:Artículo
Palabras clave:Fixed-point index theory; Filtration pair; Isolated fixed-point; Isolating neighborhood isolating block
Materias:Ciencias > Matemáticas > Topología
Código ID:13986

[1] S. Baldwin and E. E. Slaminka. A stable/unstable ‘manifold’ theorem for area preserving homeomorphisms of two dimensions. Proc. Amer. Math. Soc. 109(3) (1990), 823–828.

[2] M. Bonino. Lefschetz index for orientation reversing planar homeomorphisms. Proc. Amer. Math. Soc. 130(7) (2002), 2173–2177.

[3] K. Borsuk. Theory of Shape (Monografie Matematyczne, 59). PWN, Warsaw, 1975.

[4] K. Borsuk. Theory of Retracts (Monografie Matematyczne, 44). PWN, Warsaw, 1967.

[5] L. E. Brouwer. Beweis des ebenen translationssatzes. Math. Ann. 72 (1912), 37–54.

[6] M. Brown. On the fixed point index of iterates of planar homeomorphisms. Proc. Amer. Math. Soc. 108 (1990), 1109–1114.

[7] M. Brown. A new proof of Brouwer’s lemma on translation arcs. Houston J. Math. 10 (1984), 35–41.

[8] R. F. Brown. The Lefschetz Fixed Point Theorem. Scott Foreman, Glenview, IL and London, 1971.

[9] P. Le Calvez. Une propriété dynamique des homéomorphismes du plan au voisinage d’un point fixe d’indice >1. Topology 38(1) (1999), 23–35.

[10] P. Le Calvez and J. C. Yoccoz. Un théoréme d’indice pour les homéomorphismes du plan au voisinage d’un point fixe. Ann. Math. 146 (1997), 241–293.

[11] C. O. Christenson and W. L. Voxman. Aspects of Topology. BCS Associates, Moscow, ID, 1998.

[12] E. N. Dancer and R. Ortega. The index or Lyapunov stable fixed points. J. Dynam. Differential Equations 6 (1994), 631–637.

[13] A. Dold. Fixed point index and fixed point theorem for Euclidean neighborhood retracts. Topology 4 (1965), 1–8.

[14] J. Franks. The Conley index and non-existence of minimal homeomorphisms. Illinois J. Math. 43(3) (1999), 457–464.

[15] J. Franks and D. Richeson. Shift equivalence and the Conley index. Trans. Amer. Math. Soc. 352(7) (2000), 3305–3322.

[16] M. Handel. There are no minimal homeomorphisms of the multipunctured plane. Ergod. Th. & Dynam. Sys. 12 (1992), 75–83.

[17] M.W. Hirsch. Fixed-point indices, homoclinic contacts, and dynamics of injective planar maps. Michigan Math. J. 47 (2000), 101–108.

[18] B. Kerékjártó. Voresungen über Topologie (I). Springer, Berlin, 1923.

[19] R. D. Nussbaum. The Fixed Point Index and some Applications. Séminaire de Mathématiques supérieures, Les Presses de L’Université de Montréal, 1985.

[20] S. Pelikan and E. E. Slaminka. A bound for the fixed point index of area-preserving homeomorphisms of two-manifolds. Ergod. Th. & Dynam. Sys. 7 (1987), 463–479.

[21] F. R. Ruiz del Portal and J. M. Salazar. Fixed point index of iterations of local homeomorphisms of the plane: a Conley-index approach. Topology 41 (2002), 1199–1212.

[22] M. Shub and D. Sullivan. A remark on the Lefschetz fixed point formula for differentiable maps. Topology 13 (1974), 189–191.

[23] C. P. Simon. A bound for the fixed point index of an area-preserving map with applications to mechanics. Invent. Math. 26 (1974), 187–200.

Depositado:07 Dic 2011 12:08
Última Modificación:07 Dic 2011 12:08

Sólo personal del repositorio: página de control del artículo