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arXiv 2010.129012020-10math.DS

Pointwise periodic maps with quantized first integrals

Anna Cima, Armengol Gasull, Víctor Mañosa, Francesc Mañosas

备注：: 46 pages, 20 figures
发表信息：: Commun Nonlinear Sci Numer Simulat 108 (2022) 106150 (26 pages)
DOI：: 10.1016/j.cnsns.2021.106150

英文摘要：

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.

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