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

Corinna Ulcigrai

Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana (2018)

  • Volume: 3, Issue: 1, page 13-30
  • ISSN: 2499-751X

Abstract

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Mathematical billiards are an idealization of the game of pool. Many systems in physics, for example in mechanics or thermodynamics, can be described by mathematical billiards. Billiards provide also a mathematical model of chaotic behaviour, which may display several different chaotic features. How much chaotic a billiard is, depends mostly on the shape of the billiard table. In this introductory article on billiards we will focus especially on the behaviour of trajectories in a class of polygonal billiards (rational ones), both bounded and infinite (such as the well known Ehrenfest model). We will try to convey some of the mathematical tools which were used to study chaotic features, such as unfolding and renormalization.

How to cite

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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 3.1 (2018): 13-30. <http://eudml.org/doc/294061>.

@article{Ulcigrai2018,
abstract = {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.},
author = {Ulcigrai, Corinna},
journal = {Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana},
language = {ita},
month = {4},
number = {1},
pages = {13-30},
publisher = {Unione Matematica Italiana},
title = {Biliardi matematici, caos e ciambelle “infinite”: perché i matematici “giocano” a biliardo, dai poligoni al modellodi Ehrenfest},
url = {http://eudml.org/doc/294061},
volume = {3},
year = {2018},
}

TY - JOUR
AU - Ulcigrai, Corinna
TI - Biliardi matematici, caos e ciambelle “infinite”: perché i matematici “giocano” a biliardo, dai poligoni al modellodi Ehrenfest
JO - Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana
DA - 2018/4//
PB - Unione Matematica Italiana
VL - 3
IS - 1
SP - 13
EP - 30
AB - 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.
LA - ita
UR - http://eudml.org/doc/294061
ER -

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