# Attractors with vanishing rotation number

Rafael Ortega; Francisco Ruiz del Portal

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 6, page 1569-1590
- ISSN: 1435-9855

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topOrtega, 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 -

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