The effect of inversely unstable solutions on the attractor of the forced pendulum equation with friction

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6 Citations (Scopus)

Abstract

Consider the attractor A of a periodically forced equation of pendulum type with linear friction, in the cylinder. Levi and independently Min, Xian and Jinyan show that if the friction coefficient is larger than a certain bound then A is homeomorphic to the circle. We shall give a topological version of the definition of inversely unstable solution of N. Levinson and show that the appearance of such solutions imply that A is not homeomorphic to the circle. As an application we shall show that the bounds on the friction coefficient obtained before are optimal.

Original languageEnglish
Pages (from-to)351-365
Number of pages15
JournalJournal Of Differential Equations
Volume212
Issue number2
DOIs
Publication statusPublished - 15 May 2005

Keywords

  • Attractor
  • Inversely unstable solution
  • Pendulum
  • Rotation number

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