PreprintULTRADISCRETE CONNECTION MATRICES OVER A TROPICAL SEMIRINGChris OrmerodAbstractWe consider linear problems associated with integrable ultradiscrete equations. In this paper, we study systems of linear difference equations over a tropical semiring. We prove that the fundamental solutions and monodromy matrix is welldefined for a class of such inear equations over the invertible maxplus algebra. We then proceed to extend the theory to define a funda mental solution over the maxplus algebra. As an application we consider some special forms of the ultradiscrete Riccati equation and show it possesses a fundamental solution.Keywords: Ultradiscrete, maxplus, monodromy, Integrable. AMS Subject Classification: Primary 39A13; secondary 33E17, 37B15.
