COMPUTING TOPOLOGICAL INVARIANTS IN BOUNDARY VALUE PROBLEMS REDUCIBLE TO DIFFERENCE EQUATIONS

Abstract

Among boundary values problems (BVP) for partial differential equations there are certain classes of problems reducible to difference equations. Effective study of such problems has became possible in the last 20-30 years owing to appreciable advances done also in the theory of difference equations with discrete time, specifically given by one-dimensional maps. Here we apply how this reduction method may be used in simple nonlinear BVP, determined by a bimodal map. We consider two-dimensional linear hyperbolic system with constant coefficients, with nonlinear boundary conditions and usual initial conditions. The objective is to characterize the dependence of the motions of the vortice solutions with the topological invariants of the bimodal map.