The Statistics of the Trajectory in a Certain Billiard in a Flat Two-torus
نویسندگان
چکیده
Abstract. We study a billiard in a modified square with pockets of small size ε. The length, respectively the number of reflections in the side cushions, of the trajectory that originates at one corner under angle θ is denoted by lε(θ), respectively by Rε(θ). We prove that the probability measures associated with the random variables εlε and εRε are convergent as ε ց 0 and provide explicit formulas for the limits.
منابع مشابه
The Statistics of the Trajectory of a Certain Billiard in a Flat Two-torus
Abstract. We consider a billiard in the punctured torus obtained by removing a small disk of radius ε > 0 from the flat torus T, with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity ω only. Let τ̃ε(ω), and respectively R̃ε(ω), denote the first exit time (length of the trajectory), and respectively the number of collisions wit...
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