The periodically forced KdVB and extended KdVB equations are considered. We investigate the structure of the totality of steady profiles. The existence of profiles that are close to any shuffling of two basic profiles is proved, and hence the existence of spatially chaotic and recurrent solutions. The proofs are based on topological degree theory to analyse chaotic behaviour. These proofs combine ideas suggested by P. Zgliczyński (
Zgliczyński 1996
Topol. Methods Nonlinear Anal
.
8
, 169–177
) with the method of topological shadowing. The results are also applicable to the classical problem of a quite general model of a forced nonlinear oscillator with viscous damping.
Abstract. Dynamical systems f in R d are studied. Let Ω ⊂ R d be a bounded open set. We will be interested in those periodic orbits such that at least one of its points lies inside Ω and at least one of its points lies outside Ω; the orbits with this property are called Ω-broken. Information about the structure of the set of Ω-broken orbits is suggested; results are formulated in terms of topological degree theory.
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