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July  2006, 14(3): 533-547. doi: 10.3934/dcds.2006.14.533

One-dimensional attractor for a dissipative system with a cylindrical phase space

Rogério Martins 1,

1. 

Dep. Matemática, FCT, Universidade Nova de Lisboa and CMAF, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

Received  September 2004 Revised  June 2005 Published  December 2005

Consider an attractor of a dissipative non-autonomous system with one angle coordinate. We give conditions for this attractor to be homeomorphic to the circle where we find connections with the work of R. A. Smith. Several applications are studied, such as: the forced pendulum, discretizations of the sine-Gordon equation, n'th order equations, among others.
Keywords: pendulum, cylindrical phase space., Attractor, dissipative systems.
Mathematics Subject Classification: Primary: 34A34, 34C15, 34D45; Secondary: 70K4.
Citation: Rogério Martins. One-dimensional attractor for a dissipative system with a cylindrical phase space. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 533-547. doi: 10.3934/dcds.2006.14.533
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