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 language | English |
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Pages (from-to) | 351-365 |
Number of pages | 15 |
Journal | Journal Of Differential Equations |
Volume | 212 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 May 2005 |
Keywords
- Attractor
- Inversely unstable solution
- Pendulum
- Rotation number