Two Dimensional Poincare Maps constructed through Ginzburg-Landau Theory of critical phenomena in Physics

Abstract

Based on the saddle point approximation in G-L theory of the critical phenomena we construct two-dimensional Poincare maps which describe the symmetry breaking (SB) and the tricritical crossover phenomenon in Physics. The phase space diagrams of these maps are in agreement with the theoretical predictions. A correction in these maps close to the critical point for small values of the order parameter is attempted. Finally we demonstrate that numerical experiments verify the correctness of these maps.