The Iris Billiard: Critical Geometries for Global Chaos

Gregory Page, Charles Antoine, Carl P Dettmann , Julian Talbot*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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We introduce the Iris Billiard, consisting of a point particle enclosed by a unit circle enclosing a central scattering ellipse of fixed elongation (defined as the ratio of the semi-major to the semi-minor axes). When the ellipse degenerates to a circle, the system is integrable, otherwise it displays mixed dynamics. Poincaré sections are displayed for different elongations. Recurrence plots are then applied to the long-term chaotic dynamics of trajectories launched from the unstable period-2 orbit along the semi-major axis i.e., one that initially alternately collides with the ellipse and the circle. We obtain numerical evidence of a set of critical elongations at which the system transitions to global chaos. The transition is characterized by an endogenous escape event, E , which is the first time a trajectory launched from the unstable period-2 orbit misses the ellipse. The angle of escape, θ_esc and distance of closest approach, d_min of the escape
event are studied, and are shown to be exquisitely sensitive to the elongation. The survival probability that E has not occurred after n collisions is shown to follow an exponential distribution.
Original languageEnglish
Article number123105 (2020)
Number of pages23
Publication statusPublished - 1 Dec 2020

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