Filimonov, A.; Mao, X.; Maslov, S. Splash effect and ergodic properties of solution of the classic difference-differential equation. (English) Zbl 0965.37005 J. Difference Equ. Appl. 6, No. 3, 319-328 (2000). The classical model of movement of \(N\) identical material points along a circle with large radius is considered. This model is going back to Bernoulli and Lagrange and can be described by the following difference-differential equation: \[ m\ddot{W}_j=c(W_{j+1}-2W_j+W_{j-1})+G_j,\qquad j=1,\ldots,N, \] with periodic boundary condition \(W_{j+N}=W_j. \) The relationship between ergodic properties of this model and the splash effect [see A. M. Filimonov, C. R. Acad. Sci., Paris, Sér. I 315, 957-961 (1992; Zbl 0761.73053)] is described. Reviewer: Natalia Medvedeva (Chelyabinsk) Cited in 1 Document MSC: 37A25 Ergodicity, mixing, rates of mixing 34K10 Boundary value problems for functional-differential equations 58K55 Asymptotic behavior of solutions to equations on manifolds 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) Keywords:differential-difference equation; splash effect; chaotic properties Citations:Zbl 0761.73053 PDFBibTeX XMLCite \textit{A. Filimonov} et al., J. Difference Equ. Appl. 6, No. 3, 319--328 (2000; Zbl 0965.37005) Full Text: DOI References: [1] Anderson P.W., Nobel Lecture 8 (1977) [2] Bernoulli D., Memoires de la’ academie Royale de Berlin 9 pp 147– (1753) [3] Filimonov A.M., Computes Rendus Acad. Sci. Paris t 313 pp 961– (1991) [4] Filimonov A.M., The case of multiple frequencies. Computes Rendus Acad. Sci. Paris t 315 pp 957– (1992) · Zbl 0761.73053 [5] DOI: 10.1080/10236199608808075 · Zbl 0882.34068 · doi:10.1080/10236199608808075 [6] DOI: 10.1080/10236199808808125 · Zbl 0907.34050 · doi:10.1080/10236199808808125 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.