Pointwise periodic maps with quantized first integrals
arXiv:2010.12901 · doi:10.1016/j.cnsns.2021.106150
Abstract
We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete, thus quantized. Furthermore, the level sets are bounded sets whose interior is formed by a finite number of open tiles of certain regular or uniform tessellations. The action of the maps on each invariant set of tiles is described geometrically.
46 pages, 20 figures