Statistics of visits to zero angle corners of billiards
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2000Tipo
Abstract
Consider a Sinai billiard table Q (bounded region of the plane, with a finite number of dispersing boundaries âQ;) such that two circular pieces of the boundary are tangent at C . Consider the dynarnical systE'm T describing the free motion of a point mass in Q, with elastic refiections on the boundary (angle of incidence with the normal to the curve equal to the angle of reflection). V e prove tha.t the sequence of successive entrance times in a certain small neighbourhooà of the comer C conv ...
Consider a Sinai billiard table Q (bounded region of the plane, with a finite number of dispersing boundaries âQ;) such that two circular pieces of the boundary are tangent at C . Consider the dynarnical systE'm T describing the free motion of a point mass in Q, with elastic refiections on the boundary (angle of incidence with the normal to the curve equal to the angle of reflection). V e prove tha.t the sequence of successive entrance times in a certain small neighbourhooà of the comer C converges in law, when suitable normalizeà, to a Poisson point process. ...
Contido em
Cadernos de matemática e estatística. Série A, Trabalho de pesquisa. Porto Alegre. N. 55 (abr. 2000), p. 1-20
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