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Hyperbolic polygonal billiards with finitely many ergodic SRB measures

Published online by Cambridge University Press:  14 March 2017

GIANLUIGI DEL MAGNO ,
JOÃO LOPES DIAS ,
PEDRO DUARTE  and
JOSÉ PEDRO GAIVÃO
GIANLUIGI DEL MAGNO
Affiliation:
Universidade Federal da Bahia, Instituto de Matemática, Avenida Adhemar de Barros, Ondina, 40170–110 Salvador, BA, Brasil email gdelmagno@ufba.br
JOÃO LOPES DIAS
Affiliation:
Departamento de Matemática and CEMAPRE, ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200–781 Lisboa, Portugal email jldias@iseg.ulisboa.pt
PEDRO DUARTE
Affiliation:
Departamento de Matemática and CMAF, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edificio C6, Piso 2, 1749–016 Lisboa, Portugal email pmduarte@fc.ul.pt
JOSÉ PEDRO GAIVÃO
Affiliation:
Departamento de Matemática and CEMAPRE, ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200–781 Lisboa, Portugal email jpgaivao@iseg.ulisboa.pt
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Abstract

We study polygonal billiards with reflection laws contracting the angle of reflection towards the normal. It is shown that if a polygon does not have parallel sides facing each other, then the corresponding billiard map has finitely many ergodic Sinai–Ruelle–Bowen measures whose basins cover a set of full Lebesgue measure.

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 6 , September 2018 , pp. 2062 - 2085
Copyright
© Cambridge University Press, 2017 

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