Bambusi, Dario and Maspero, Alberto:
Sistemi integrabili infinito dimensionali e loro perturbazioni
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana Serie 1 2 (2017), fasc. n.3, p. 309-326, (Italian)
pdf (410 Kb), djvu (324 Kb). | MR 3753847
Sunto
Durante gli ultimi 50 anni, sono stati fatti enormi progressi nella comprensione del comportamento qualitativo di equazioni a derivate parziali non lineari. In modo specifico, l'estensione a questo ambito dei metodi della meccanica Hamiltoniana ha permesso dapprima di capire che esiste un'intera classe di equazioni, chiamate ``integrabili'', le cui soluzioni hanno sempre carattere ricorrente, e successivamente di cominciare a comprendere ciò che avviene quando queste equazioni sono perturbate e danno luogo a sistemi in cui possono coesistere comportamenti regolari e comportamenti turbolenti. Nel nostro articolo, presenteremo alcuni dei risultati di questa teoria, a partire dalle sue origini fino a oggi, e discuteremo alcuni dei più importanti problemi aperti.
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Con il contributo del Ministero per i Beni e le Attività Culturali