Bifurcation structures in two-dimensional maps: The endoskeletons of shrimps

- Bifurcation structures in nonlinear systems display complex geometries called shrimps.
- In one-dimensional maps, superstable cycles provide a skeleton for the shrimps.
- In two-dimensional maps, the trace of the stability matrix defines the skeleton.
- The skeleton for the Hénon map is computed using continuation methods.
- There are differences in the topology of skeletons in one- and two-dimensional maps.