Graphs emerging from the solutions to the periodic discrete Toda equation over finite fields
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Abstract
The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing a equivalence class of cyclic permutations to the initial values. We proved that the graphs are bidirectional and that they are composed of several arrays of complete graphs connected at one of their vertices. The condition for the graphs to be bidirectional is studied for general discrete equations.<br/>MSC2010: 37K10, 37P05, 37P25, 37J35
Journal

 Nonlinear Theory and Its Applications, IEICE

Nonlinear Theory and Its Applications, IEICE 7(3), 338353, 2016
The Institute of Electronics, Information and Communication Engineers