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首页> 外文期刊>Open Mathematics >Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers : Open Mathematics
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Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers : Open Mathematics

机译：带有Lefschetz数的周期序列的简单连通流形的光滑自映射的周期点数的最小化：开放数学

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摘要

Let f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of f.In this paper the invariant J[f] is computed for self-maps of 4-manifold M with dimH 2(M; ?) ≤ 4 and estimated for other types of manifolds. We also use J[f] to compare minimization of the number of periodic points in smooth and in continuous categories.
机译：令f为m维的平滑自映射，m≥4，平滑闭合连通和简单连通歧管，r为固定自然数。对于具有Lefschetz周期序列的迭代次数的图类，作者在[Graff G.，Kaczkowska A.中介绍，减少具有Lefschetz周期序列的简单连通流形的光滑同伦类自映射的周期点数数字，安波兰人。数学。 （在印刷中）]拓扑不变性J [f]等于f的光滑同伦类中周期小于或等于r的最小周期点的数目。具有dimH 2（M;？）≤4的4流形M的自映射，并针对其他类型的歧管进行了估计。我们还使用J [f]比较平滑类别和连续类别中的周期点数量的最小化。

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