On planar zero-diagonal and zero-trace iterated maps

ABSTRACT

We call an iterated map zero-diagonal, if it has a zero-diagonal Jacobi matrix for all x,y. Similarly, zero-trace iterated maps are the maps with zero-trace Jacobi matrix. In this paper, we present some of the geometric and algebraic properties of zero-diagonal planar maps. However, the main focus of this paper is the analysis of the zero-trace planar maps by linear transforming them to a zero-diagonal ones. Some sufficient conditions for the transformation are obtained. Stability for non-hyperbolic fixed points, two types of codim-2 bifurcations, and the local/global invariant manifolds for zero-diagonal and zero-trace maps are investigated.

KEYWORDS:

• Zero-diagonal maps
• zero-trace maps
• degenerate points
• 1:4 resonance
• fold-flip bifurcation
• codim-2 bifurcations

Disclosure statement

No potential conflict of interest was reported by the author.