标题： 分段线性映射中的次级同宿连接和无限多个共存吸引子 显示英文标题

标题： Subsumed homoclinic connections and infinitely many coexisting attractors in piecewise-linear maps

摘要： 我们建立了无限多个渐近稳定的周期解与$N$维分段线性连续映射中包含的同宿连接之间的等价性。 这些特征是三阶现象。 周期解是单圈的：每个解都涉及一次远离中心马鞍型周期解的运动。 同宿连接是包含的，因为马鞍解的不稳定流形的一个分支完全包含在其稳定流形中。 结果通过使用周期解和稳定与不稳定流形的组成部分的精确表达式进行证明，这是因为映射是分段线性的，所以这些表达式是可用的。 我们还描述了一种在映射参数空间中寻找这种现象的实用方法，并用三维边界碰撞规范形式来说明结果。 显示英文摘要

摘要： We establish an equivalence between infinitely many asymptotically stable periodic solutions and subsumed homoclinic connections for $N$-dimensional piecewise-linear continuous maps. These features arise as a codimension-three phenomenon. The periodic solutions are single-round: they each involve one excursion away from a central saddle-type periodic solution. The homoclinic connection is subsumed in the sense that one branch of the unstable manifold of the saddle solution is contained entirely within its stable manifold. The results are proved by using exact expressions for the periodic solutions and components of the stable and unstable manifolds which are available because the maps are piecewise-linear. We also describe a practical approach for finding this phenomenon in the parameter space of a map and illustrate the results with the three-dimensional border-collision normal form.