Attractors with vanishing rotation number

Ortega, Rafael, and Ruiz del Portal, Francisco. "Attractors with vanishing rotation number." Journal of the European Mathematical Society 013.6 (2011): 1569-1590. <http://eudml.org/doc/277701>.

@article{Ortega2011,
abstract = {Given an orientation-preserving homeomorphism of the plane, a rotation number can be associated with each locally attracting fixed point. Assuming that the homeomorphism is dissipative and the rotation number vanishes we prove the existence of a second fixed point. The main tools in the proof are Carath´eodory prime ends and fixed point index. The result is applicable to some concrete problems in the theory of periodic differential equations.},
author = {Ortega, Rafael, Ruiz del Portal, Francisco},
journal = {Journal of the European Mathematical Society},
keywords = {planar attractor; prime end; fixed point index; global asymptotic stability; invariant ray; periodic differential equation; extinction; planar attractor; prime end; fixed point index; global asymptotic stability; invariant ray; periodic differential equation; extinction},
language = {eng},
number = {6},
pages = {1569-1590},
publisher = {European Mathematical Society Publishing House},
title = {Attractors with vanishing rotation number},
url = {http://eudml.org/doc/277701},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Ortega, Rafael
AU - Ruiz del Portal, Francisco
TI - Attractors with vanishing rotation number
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 6
SP - 1569
EP - 1590
AB - Given an orientation-preserving homeomorphism of the plane, a rotation number can be associated with each locally attracting fixed point. Assuming that the homeomorphism is dissipative and the rotation number vanishes we prove the existence of a second fixed point. The main tools in the proof are Carath´eodory prime ends and fixed point index. The result is applicable to some concrete problems in the theory of periodic differential equations.
LA - eng
KW - planar attractor; prime end; fixed point index; global asymptotic stability; invariant ray; periodic differential equation; extinction; planar attractor; prime end; fixed point index; global asymptotic stability; invariant ray; periodic differential equation; extinction
UR - http://eudml.org/doc/277701
ER -