Iterated-map approach to die tossing

Rasmus Feldberg, Maciej Szymkat, Carsten Knudsen, Erik Mosekilde

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Abstract

Nonlinear dissipative mapping is applied to determine the trajectory of a two-dimensional die thrown onto an elastic table. The basins of attraction for different outcomes are obtained and their distribution in the space of initial conditions discussed. The system has certain properties in common with chaotic systems. However, a die falls to rest after a finite number of impacts, and therefore the system has a finite sensitivity to the initial conditions. Quantitative measures of this sensitivity are proposed and their variations with the initial momentum and orientation of the die investigated.
Original languageEnglish
JournalPhysical Review A
Volume42
Issue number8
Pages (from-to)4493-4502
ISSN2469-9926
DOIs
Publication statusPublished - 1990

Bibliographical note

Copyright (1990) by the American Physical Society.

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