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An important property of the elliptic flowers is that these billiard tables are merely connected. Besides, clearly only such elliptic flowers would be probably the most straightforward to construct in the experimental labs. Moreover, the corresponding billiard tables are simply linked in difference with many attempts to build billiards with fascinating and/or exotic dynamics by placing inside billiard tables varied "scatterers" with funny shapes. However, in difference with circular flowers, which always have chaotic and ergodic dynamics, this class of billiards demonstrates a big number of attainable behaviors. We introduce a class of billiards with chaotic unidirectional flows (or non-chaotic unidirectional flows with "vortices") which go round a chaotic or non-chaotic "core", the place orbits can change their orientation. Dynamics within the core additionally (as in tracks) might be chaotic or non-chaotic. A easy description of dynamics within the elliptic flowers billiards is the existence of a core surrounded by two flows (tracks) going in the other instructions, which could possibly be chaotic or have internal "vortices". We begin with the following easy Proposition. It allows to provide both easy and visual proofs, or the outcomes instantly observe from the already current ones within the mathematical principle of billiards. While being arguably probably the most ancient class of dynamical systems ever studied (what is known as now integrability of billiards in circles, was known for millennia) it stays on a forefront of the speculation of dynamical systems and their functions.

More exactly, we study the so called complete integrability in a strip between two neighboring invariant curves which we now turn to elucidate. Substitute now each of these n