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Attractors with vanishing rotation number

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Ortega, Refael and Romero Ruiz del Portal, Francisco (2011) Attractors with vanishing rotation number. Journal of the European Mathematical Society, 13 (6). pp. 1569-1590. ISSN 1435-9855

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Official URL: http://www.ems-ph.org/journals/show_pdf.php?issn=1435-9855&vol=13&iss=6&rank=2



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 Caratheodory prime ends and fixed point index. The result is applicable to some concrete problems in the theory of periodic differential equations.


Item Type:Article
Uncontrolled Keywords:Planar attractor; Prime end; Fixed point index; Global asymptotic stability; Invariant ray; Periodic differential equation; Extinction
Subjects:Sciences > Mathematics > Differential equations
ID Code:18098
Deposited On:31 Jan 2013 09:45
Last Modified:14 Dec 2018 15:10

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