Abstract

The uniform approach to the concept of geometric integrability for discrete dynamical systems on invariant plane sets is suggested. Geometric and analytic necessary and sufficient conditions for the geometric integrability of maps on invariant plane sets are proved. The solution of the coexistence problem of periodic orbits periods for these maps is given. Obtained results are applied, in particular, to description of the set of periodic orbits (least) periods of geometrically integrable maps with the quotient which is a symmetric Lorenz map.

中文翻译：

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平面上的几何可积图及其周期轨道

摘要

提出了对不变平面集上离散动力系统的几何可积性概念的统一方法。证明了地图在不变平面集上的几何可积性的几何和解析充要条件。给出了这些地图的周期轨道周期共存问题的解决方案。获得的结果特别适用于描述几何可积映射的一组周期轨道（最小）周期，其中商是对称洛伦兹映射。