RT Journal Article
T1 Index 1 fixed points of orientation reversingplanar homeomorphisms
A1 Romero Ruiz del Portal, Francisco
A1 Salazar, J. M.
AB Let U subset of R-2 be an open subset, f : U -> f (U) subset of R-2 be an orientation reversing homeomorphism and let 0 is an element of U be an isolated, as a periodic orbit, fixed point. The main theorem of this paper says that if the fixed point indices i(R2)(f, 0) = i(R2)(f(2), 0) = 1 then there exists an orientation preserving dissipative homeomorphism phi: R-2 -> R-2 such that f(2) = phi in a small neighbourhood of 0 and {0} is a global attractor for phi. As a corollary we have that for orientation reversing planar homeomorphisms a fixed point, which is an isolated fixed point for f(2), is asymptotically stable if and only if it is stable. We also present an application to periodic differential equations with symmetries where orientation reversing homeomorphisms appear naturally
PB Juliusz Schauder Center
SN 1230-3429
YR 2015
FD 2015
LK https://hdl.handle.net/20.500.14352/34979
UL https://hdl.handle.net/20.500.14352/34979
LA eng
NO Ministerio de Ciencia e Innovación (MICINN)
DS Docta Complutense
RD 10 abr 2025