It is well known from the homotopy theory of surfaces that an ambient isotopy does not change the homotopy type of a closed curve. Using the language of dynamical systems, this means that an arc in the space of diffeomorphisms that joins two isotopic diffeomorphisms with invariant closed curves in distinct homotopy classes must go through bifurcations. A scenario is described which changes the homotopy type of the closure of the invariant manifold of a saddle point of a polar diffeomorphism of a 2-torus to any prescribed homotopically nontrivial type. The arc constructed in the process is stable and does not change the topological conjugacy class of the original diffeomorphism. The ideas that are proposed here for constructing such an arc for a 2-torus can naturally be generalized to surfaces of greater genus. Bibliography: 32 titles.

中文翻译：

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改变表面微分同胚不变鞍流形闭包同伦型的分岔

从表面的同伦理论众所周知，环境同位素不会改变闭合曲线的同伦类型。使用动力系统的语言，这意味着微分同胚空间中连接两个同伦类中具有不变闭合曲线的同位素微分同胚的弧必须经历分叉。描述了一种场景，该场景将 2-环面的极微分同胚的鞍点的不变流形的闭包的同伦类型更改为任何规定的同伦非平凡类型。在此过程中构造的弧是稳定的，不会改变原有微分同胚的拓扑共轭类。这里提出的为 2-环面构造这样的弧的想法可以自然地推广到更大亏格的表面。参考书目：32 种。