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Global periodicity and complete integrability of discrete dynamical systems |
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| Authors: | Anna Cima Armengol Gasull Víctor Mañosa |
| Affiliation: | 1. Department de Matemàtiques, Facultat de Ciències , Universitat Autònoma de Barcelona , 08193, Bellaterra, Barcelona, Spain cima@mat.uab.es gasull@mat.uab.es;3. Department de Matemàtiques, Facultat de Ciències , Universitat Autònoma de Barcelona , 08193, Bellaterra, Barcelona, Spain;4. Department de Matemàtica Aplicada III , Control, Dynamics and Applications Group (CoDALab) , Universitat Politècnica de Catalunya, Colom 1 , 08222, Terrassa, Spain |
| Abstract: | Consider the discrete dynamical system generated by a map F. It is said that it is globally periodic if there exists a natural number p such that F p (x)=x for all x in the phase space. On the other hand, it is called completely integrable if it has as many functionally independent first integrals as the dimension of the phase space. In this paper, we relate both concepts. We also give a large list of globally periodic dynamical systems together with a complete set of their first integrals, emphasizing the ones coming from difference equations. |
| Keywords: | Globally periodic discrete dynamical system First integrals Completely integrable systems Difference equations Invariants for difference equations |