报告题目: |
Topological Methods of Finding Periodic Points |
报告人: |
Prof. Waclaw Marzantowicz |
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Adam Mickiewicz University
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报告时间: |
2010-10-14 15:30 |
报告地点: |
理科楼1304报告厅 |
主办单位: |
数学科学系 |
简介: |
Let $f : X \to X$ be a continuous map of compact closed manifold. A point $x \in X$ is called a periodic point of $f$ of period $n$ if there exists $n \in\mathbb{N}$ such that $f^n(x) = x$. We will present a survey of methods based on the classical Lefschetz and Nielsen theories which estimate (from below) the number periodic points of period n and describe appearing minimal periods. By their constructions these methods give invariants which are preserved by a homotopy of map. Consequently they are rough but on the other side stable, i.e. these invariants are preserved by a deformation in particular by a small perturbation of map. A combination of these methods with another assumptions on $f$, as $C^1$-smoothness, symmetry, analyticity let us to improve essentially results. |
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