This paper deals with perturbed dynamical systems of the form: −u¨+u=∇V(u)+ε∇uW(t,u) where u(t)∈Rn(n⩾1). By means of a variational approach the existence of multibump homoclinics is proved under general assumptions on the Melnikov function. As a particular case, if (W; u) is T-periodic, the existence of approximate and complete Bernoulli shift structures is proved. An application to partial differential equations is also given.
Homoclinics and chaotic behaviour for perturbed second order systems / Berti, M.; Bolle, P.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 176:1(1999), pp. 323-378. [10.1007/BF02506001]
Homoclinics and chaotic behaviour for perturbed second order systems
Berti, M.;
1999-01-01
Abstract
This paper deals with perturbed dynamical systems of the form: −u¨+u=∇V(u)+ε∇uW(t,u) where u(t)∈Rn(n⩾1). By means of a variational approach the existence of multibump homoclinics is proved under general assumptions on the Melnikov function. As a particular case, if (W; u) is T-periodic, the existence of approximate and complete Bernoulli shift structures is proved. An application to partial differential equations is also given.File in questo prodotto:
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