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We introduce a class of billiards with chaotic unidirectional flows (ornon-chaotic unidirectional flows with "vortices") which go around a chaotic ornon-chaotic "core", where orbits can change their orientation. Moreover, thecorresponding billiard tables are simply connected in difference with manyattempts to build billiards with interesting and/or exotic dynamics by puttinginside billiard tables various "scatterers" with funny shapes. Therefore thebilliards in this new class are amenable to experimental studies in physicslabs as well as to the rigorous mathematical ones, which may shed a new lighton understanding of classical and quantum dynamics of Hamiltonian systems.

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