Chenciner Bifurcation Presenting a Further Degree of Degeneration

Abstract

Chenciner bifurcation appears for some two-dimensional systems with discrete time having two independent variables. Investigated here is a special case of degeneration where the implicit function theorem cannot be used around the origin, so a new approach is necessary. In this scenario, there are many more bifurcation diagrams than in the two non-degenerated cases. Several numerical simulations are presented.

Keywords

• degeneracy
• bifurcation
• Chenciner
• discrete systems