Elliptic Flowers: simply connected billiard tables with chaotic or non-chaotic flows moving around chaotic or non-chaotic cores

The paper proves, for special one-layer elliptic flowers (SOL EF) over regular polygons with n ≥ 5, the existence of exactly three positive-measure ergodic components: two chaotic (hyperbolic, ergodic) tracks and a chaotic (hyperbolic, ergodic) core. This is established via Theorem 3.2 (two positive-measure tracks), Theorem 3.7 (hyperbolic/ergodic core for n ≥ 5 via defocusing), Theorem 3.8 (hyperbolic/ergodic tracks under absolute focusing), and Theorem 3.9 (combining these to obtain exactly three components) . The model’s construction and argument align closely: it builds SOL EF over regular n-gons with petal arcs chosen to ensure inter-petal defocusing and absolute focusing of each petal, deduces hyperbolicity of the core and of each track, and appeals to local-ergodicity results to conclude ergodicity of each component, yielding exactly three components. Minor differences are present (e.g., the model invokes C3-closeness and a specific local ergodicity reference), but the logic is essentially the same as the paper’s proof sketch. The paper also notes concrete SOL EF examples (Wild Rose for n=5, Narcissus for n=6) with the desired properties .