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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| Veröffentlicht in: | Communications in nonlinear science & numerical simulation 2020-12, Vol.91, p.105440, Article 105440 |
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| container_title | Communications in nonlinear science & numerical simulation |
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| creator | da Costa, Diogo Ricardo Palmero, Matheus S. Méndez-Bermúdez, J.A. Iarosz, Kelly C. Szezech Jr, José D. Batista, Antonio M. |
| description | 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. |
| doi_str_mv | 10.1016/j.cnsns.2020.105440 |
| format | Article |
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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. 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Moreover, for small tilting, this phase space shows a web-like hierarchical structure.</description><subject>Chaos</subject><subject>Chaos theory</subject><subject>Mathematical analysis</subject><subject>Mushroom billiards</subject><subject>Mushrooms</subject><subject>Nonlinear dynamics</subject><subject>Phase transitions</subject><subject>Structural hierarchy</subject><subject>Webs</subject><issn>1007-5704</issn><issn>1878-7274</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouK7-Ai8Fz10nTfoRwYOIq8KClxWPIR8TmtqPNemK_nu71rOnGYb3mWEeQi4prCjQ4rpZmT72cZVBdpjknMMRWdCqrNIyK_nx1AOUaV4CPyVnMTYwUSLnC7Le-nZEm9ZqTLp9rMMwdIn2betVsPEmeUOdtv4dk9pjUMHU3qg26fwX2mRXq4hJ3CmD5-TEqTbixV9dktf1w_b-Kd28PD7f321SwxgdU-eqEpiG3FCtXFW4gjPBsdKloJmhgExYgYAWNEUNjmUcqdWCgiscE4ItydW8dxeGjz3GUTbDPvTTSZnxgha0yqtiSrE5ZcIQY0And8F3KnxLCvIgTDbyV5g8CJOzsIm6nSmcHvic3pXReOwNWh_QjNIO_l_-BxeudIg</recordid><startdate>202012</startdate><enddate>202012</enddate><creator>da Costa, Diogo Ricardo</creator><creator>Palmero, Matheus S.</creator><creator>Méndez-Bermúdez, J.A.</creator><creator>Iarosz, Kelly C.</creator><creator>Szezech Jr, José D.</creator><creator>Batista, Antonio M.</creator><general>Elsevier B.V</general><general>Elsevier Science Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-9134-0753</orcidid><orcidid>https://orcid.org/0000-0002-1748-9901</orcidid><orcidid>https://orcid.org/0000-0002-5899-0591</orcidid></search><sort><creationdate>202012</creationdate><title>Tilted-hat mushroom billiards: Web-like hierarchical mixed phase space</title><author>da Costa, Diogo Ricardo ; Palmero, Matheus S. ; Méndez-Bermúdez, J.A. ; Iarosz, Kelly C. ; Szezech Jr, José D. ; Batista, Antonio M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c331t-ff8703b05c1baf86f64394e8b7912c10e39d9e0ed0b1eb0f324e1db910f6f3993</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Chaos</topic><topic>Chaos theory</topic><topic>Mathematical analysis</topic><topic>Mushroom billiards</topic><topic>Mushrooms</topic><topic>Nonlinear dynamics</topic><topic>Phase transitions</topic><topic>Structural hierarchy</topic><topic>Webs</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>da Costa, Diogo Ricardo</creatorcontrib><creatorcontrib>Palmero, Matheus S.</creatorcontrib><creatorcontrib>Méndez-Bermúdez, J.A.</creatorcontrib><creatorcontrib>Iarosz, Kelly C.</creatorcontrib><creatorcontrib>Szezech Jr, José D.</creatorcontrib><creatorcontrib>Batista, Antonio M.</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in nonlinear science & numerical simulation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>da Costa, Diogo Ricardo</au><au>Palmero, Matheus S.</au><au>Méndez-Bermúdez, J.A.</au><au>Iarosz, Kelly C.</au><au>Szezech Jr, José D.</au><au>Batista, Antonio M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Tilted-hat mushroom billiards: Web-like hierarchical mixed phase space</atitle><jtitle>Communications in nonlinear science & numerical simulation</jtitle><date>2020-12</date><risdate>2020</risdate><volume>91</volume><spage>105440</spage><pages>105440-</pages><artnum>105440</artnum><issn>1007-5704</issn><eissn>1878-7274</eissn><abstract>Mushroom billiards are formed, generically, by a semicircular hat attached to a rectangular stem. 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| subjects | Chaos Chaos theory Mathematical analysis Mushroom billiards Mushrooms Nonlinear dynamics Phase transitions Structural hierarchy Webs |
| title | Tilted-hat mushroom billiards: Web-like hierarchical mixed phase space |
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