We consider a class of billiard tables obtained by intersecting elliptical domains x2/a2 + y2 ≤ 1, a > 1 with horizontal strips |y| ≤ h < 1. The boundary of these tables consists of two elliptical arcs connected by two parallel straight segments. We prove that the billiards in these tables have non-vanishing Lyapunov exponents for h < min(1/a, 1/√2), and are ergodic for h < 1/√1 +a2.
Ergodicity of a class of truncated elliptical billiards
Del Magno G.
2001-01-01
Abstract
We consider a class of billiard tables obtained by intersecting elliptical domains x2/a2 + y2 ≤ 1, a > 1 with horizontal strips |y| ≤ h < 1. The boundary of these tables consists of two elliptical arcs connected by two parallel straight segments. We prove that the billiards in these tables have non-vanishing Lyapunov exponents for h < min(1/a, 1/√2), and are ergodic for h < 1/√1 +a2.File in questo prodotto:
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