Piecewise linear maps with heterogeneous chaos

Chaotic dynamics can be quite heterogeneous in the sense that some regions are unstable more directions than other regions. When trajectories wander between these regions, is complicated. We say a chaotic invariant set when arbitrarily close to each point of there different periodic points with numbers dimensions. call such chaos (or hetero-chaos), While we believe it common for physical systems hetero-chaotic, few explicit examples have been proved hetero-chaotic. Here present two dynamical particularly simple and tractable computer. It will give intuition as how complex even be. Our maps one dense whose orbits 1D another 2D unstable. Moreover, they ergodic relative Lebesgue measure.