We consider a discrete-time -equivariant cubic dynamical system depending upon a real parameter. The system under consideration is a particular case of a discrete analogue to the principal -equivariant differential equations. We rigorously prove that the system has an asymptotically stable heteroclinic cycle, relatively to an open subset of a compact subspace of the plane, for values of the parameter in the interval . We explore properties of the omega-limit sets for the points attracted by the heteroclinic cycle.

中文翻译：

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离散时间等变三次动力系统中渐近稳定的异宿环

我们考虑依赖于实参数的离散时间等变三次动力系统。所考虑的系统是主等变微分方程的离散模拟的特殊情况。我们严格证明，对于区间 中的参数值，相对于平面紧凑子空间的开子集，系统具有渐近稳定的异宿环。我们探索了异宿环吸引的点的欧米茄极限集的性质。