"Non UBC"@en .
"DSpace"@en .
"Dettmann, Carl"@en .
"2018-09-17T05:00:17Z"@* .
"2018-03-20T11:10"@en .
"In dynamical systems with divided phase space, the vicinity of the\nboundary between regular and chaotic regions is often \"sticky,\" that\nis, trapping orbits from the chaotic region for long times. Here, we\ninvestigate the stickiness in the simplest mushroom billiard, which\nhas a smooth such boundary, but surprisingly subtle behaviour. As a\nmeasure of stickiness, we investigate P(t), the probability of\nremaining in the mushroom cap for at least time t given uniform\ninitial conditions in the chaotic part of the cap. The stickiness is\nsensitively dependent on the radius of the stem r via the Diophantine\nproperties of rho = (2/pi) arccos r. Almost all rho give rise to\nfamilies of marginally unstable periodic orbits (MUPOs) where P(t) ~\nC/t, dominating the stickiness of the boundary. After characterising\nthe set for which rho is MUPO-free, we consider the stickiness in this\ncase, and where rho also has continued fraction expansion with bounded\npartial quotients. We show that t^2 P(t) is bounded, varying\ninfinitely often between values whose ratio is at least 32/27. When\nrho has an eventually periodic continued fraction expansion, that is,\na quadratic irrational, t^2 P(t) converges to a log-periodic function.\nIn general, we expect less regular behaviour, with upper and lower\nexponents lying between 1 and 2. The results may shed light on the\nparameter dependence of boundary stickiness in annular billiards and\ngeneric area preserving maps."@en .
"https://circle.library.ubc.ca/rest/handle/2429/67193?expand=metadata"@en .
"38 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: The University of Bristol"@en .
"Banff (Alta.)"@en .
"10.14288/1.0372060"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Faculty"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Dynamical systems and ergodic theory"@en .
"Probability theory and stochastic processes"@en .
"Dynamical systems"@en .
"How sticky is the chaos/order boundary?"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/67193"@en .