On planar zero-diagonal and zero-trace iterated maps. (English) Zbl 1403.39018
Summary: 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.
MSC:
| 39B12 | Iteration theory, iterative and composite equations |
| 39A28 | Bifurcation theory for difference equations |
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