Garipov, R. M.; Mamontov, E. V. One-dimensional motion of inelastic balls. I: Reduction to discrete time. (English. Russian original) Zbl 0861.70015 Sib. Math. J. 34, No. 6, 1017-1026 (1993); translation from Sib. Mat. Zh. 34, No. 6, 23-33 (1993). The authors approximately construct, for some values of system collision constants, an attracting invariant set of Hausdorff dimension greater than one, and an invariant measure on it. The system consists of two balls moving along the interval between walls. The balls and walls are absolutely rigid but inelastic. During the free motion the balls accelerate proportionally to their velocity. The authors consider a Poincaré-type map and prove the kneading, and consequently ergodicity, property. Reviewer: G.Olenev (Tartu) Cited in 1 ReviewCited in 1 Document MSC: 70F35 Collision of rigid or pseudo-rigid bodies 37A99 Ergodic theory Keywords:parallel walls; attracting invariant set; Hausdorff dimension; invariant measure; Poincaré-type map; ergodicity PDFBibTeX XMLCite \textit{R. M. Garipov} and \textit{E. V. Mamontov}, Sib. Math. J. 34, No. 6, 1017--1026 (1993; Zbl 0861.70015); translation from Sib. Mat. Zh. 34, No. 6, 23--33 (1993) Full Text: DOI References: [1] R. M. Garipov, ?One-dimensional motion of absolutely rigid balls,? Izv. Akad. Nauk SSSR, No. 6, 181 (1974). [2] E. N. Lorenz, ?Deterministic nonperiodic flow,? J. Atmospheric Sci., No. 20, 130-141 (1963). · Zbl 1417.37129 [3] Ya. G. Sinaî, ?Dynamical systems with elastic reflections. Ergodic properties of scattering billiards,? Uspekhi Mat. Nauk,25, No. 2, 141-192 (1970). [4] Ya. G. Sinaî and N. I. Chernov, ?Ergodic properties of some systems of two-dimensional disks and three-dimensional balls,? Uspekhi Mat. Nauk,42, No. 3, 153-174 (1987). [5] N. N. Bogoluboff and N. M. Krylov, ?La theorie generale de la mesure dans son application a l’etude des systemes dynamiques de la mecanique non lineaire,? Ann. Math., No. 38, 65-113 (1937). · Zbl 0016.08604 [6] I. P. Kornfel’d and Ya. G. Sinaî, ?Initial notions and primary examples of ergodic theory,? in: Sovrem. Probl. Mat. Fund. Naprav. (Itogi Nauki i Tekhniki). Vol. 2 [in Russian], VINITI, Moscow, 1985, pp. 7-35. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.