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Tilted-hat mushroom billiards: Web-like hierarchical mixed phase space

Mushroom billiards are formed, generically, by a semicircular hat attached to a rectangular stem. The dynamics of mushroom billiards shows a continuous transition from integrability to chaos. However, between those limits the phase space is sharply divided in two components corresponding to regular...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2020-12, Vol.91, p.105440, Article 105440
Main Authors: da Costa, Diogo Ricardo, Palmero, Matheus S., Méndez-Bermúdez, J.A., Iarosz, Kelly C., Szezech Jr, José D., Batista, Antonio M.
Format: Article
Language:English
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Summary:Mushroom billiards are formed, generically, by a semicircular hat attached to a rectangular stem. The dynamics of mushroom billiards shows a continuous transition from integrability to chaos. However, between those limits the phase space is sharply divided in two components corresponding to regular and chaotic orbits, in contrast to most mixed phase space billiards. In this paper we show that tilting the hat of a mushroom billiard produces a highly non-trivial (i.e. non-KAM) mixed phase space. Moreover, for small tilting, this phase space shows a web-like hierarchical structure.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2020.105440