The first call for applications for the new edition of the PhD Program in Mathematics UC|UP (starting September 2018) will be open during January 02, 2018 - February 02, 2018
Introduction to the study of qualitative changes in differential equations and difference equations with parameters. These changes include, for instance, the creation and destruction of equilibrium states, changes in periodic behaviour of solutions, changes in stability and transition to chaotic behaviour. In particular: fold or saddle-node points, pitchforks, higher codimension singularities of equilibria or fixed points; bifurcation at homoclinic cycles; Hopf bifurcation; period doubling; period doubling cascades.
Special classes of dynamical systems may also be treated, for instance differential equations with symmetry or coupled cell systems.