ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We prove that the size of the finite-dimensional attractor of the damped and driven sine-Gordon equation stays small as the damping and driving amplitude become small. A decomposition of finite-dimensional attractors in Banach space is found, into a partℬ that attracts all of phase space, except sets whose finitedimensional projections have Lebesgue measure zero, and a partC that only attracts sets whose finite-dimensional projections have Lebesgue measure zero. We describe the components of the ℬ-attractor andC, which is called the “hyperbolic” structure, for the damped and driven sine-Gordon equation. ℬ is low-dimensional but the dimension ofC, which is associated with transients, is much larger. We verify numerically that this is a complete description of the attractor for small enough damping and driving parameters and describe the bifurcations of the ℬ-attractor in this small parameter region.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02101747
Permalink