Ulcigrai: Biliardi matematici, caos e ciambelle “infinite”: perché i matematici “giocano” a biliardo, dai poligoni al modellodi Ehrenfest

Ulcigrai, Corinna:
Biliardi matematici, caos e ciambelle “infinite”: perché i matematici “giocano” a biliardo, dai poligoni al modellodi Ehrenfest
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana Serie 1 3 (2018), fasc. n.1, p. 13-30, (Italian)
pdf (2.18 MB), djvu (692 Kb). | MR 3821680 | Zbl 1397.37041

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I biliardi matematici sono un'idealizzazione del gioco del biliardo. Molti modelli di sistemi fisici, ad esempio in meccanica e termodinamica, sono rappresentati da biliardi matematici. Dal punto di vista matematico, i biliardi costituiscono anche un modello molto ricco di comportamento caotico. Le proprietà matematiche che caratterizzano diversi gradi di caos dipendono fortemente dalla forma del tavolo da biliardo. In questo articolo introduttivo sui biliardi esploreremo soprattutto il comportamento delle traiettorie in certi biliardi poligonali (razionali ), sia finiti che infiniti (come il famoso modello di Ehrenfest ) e cercheremo di dare un'idea degli strumenti matematici usati per studiarli, dallo srotolamento alla rinormalizzazione.

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bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

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Referenze Bibliografiche