Coti Zelati, Vittorio and Nolasco, Margherita:
Multibump solutions for Hamiltonian systems with fast and slow forcing
Bollettino dell'Unione Matematica Italiana Serie 8 2-B (1999), fasc. n.3, p. 585-608, Unione Matematica Italiana (English)
pdf (309 Kb), djvu (287 Kb). | MR1719562 | Zbl 0940.37008
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Si dimostra l'esistenza di infinite soluzioni «multi-bump» - e conseguentemente il comportamento caotico - per una classe di sistemi Hamiltoniani del secondo ordine della forma $-\ddot{q}+q=(g_{1}(\omega t)+g_{2}(t/\omega)) V'(q)$ per $\omega$ sufficientemente piccolo. Qui $q\in \mathbb{R}^{n}$ , $g_{1}$ e $g_{2}$ sono funzioni strettamente positive e periodiche e $V$ è un potenziale superquadratico (ad esempio $V(q)=|q|^{4}$ ).
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