应兰州大学数学与统计学院李新华副教授邀请,俄罗斯国立高等经济大学Olga Pochinka教授将于2024年9月2日至9月6日访问我校并作系列学术报告。

报告题目一：Classification of three-dimensional Pixton homeomorphisms

时间：2024年9月5日（星期四）上午9: 30-10: 30

地点：大学生活动中心506报告厅

报告题目二：The regular homeomorphisms on closed manifolds

时间：2024年9月5日（星期四）上午10: 30-11: 30

地点：大学生活动中心506报告厅

报告摘要：These two talks examine the so-called regular homeomorphisms on closed manifolds. The chain-recurrent set of such discrete dynamical systems consists of a finite number of hyperbolic periodic points and they are a generalization of Morse-Smale diffeomorphisms. We will study the embedding topology of their invariant manifolds, as well as their asymptotic behavior. Let’s make sure that regular homeomorphisms that do not have saddle points exist only on the sphere and all such homeomorphisms are pairwise topologically conjugate. Next, a complete topological classification of three-dimensional Pixton homeomorphisms - homeomorphisms with a single saddle orbit will be presented. The space of such homeomorphisms decomposes into a countable number of classes of topological conjugacy and the Hopf knot is a complete invariant for them. We show how an arbitrary Hopf knot is realized by a Pixton homeomorphism, in particular a homeomorphism with wildly embedded invariant manifolds of saddle points. An immediate consequence of the implementation will be the proof of the fact that the supporting manifold for Pixton homeomorphisms is a 3-sphere.

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报告人简介

Olga Pochinka教授现任俄罗斯国立高等经济大学数学系教授，曾担任俄罗斯国立高等经济大学下诺夫哥罗德校区基础数学系系主任。她于2012年获下诺夫哥罗德国立洛巴切夫斯基大学科学博士学位。曾主持多项俄罗斯科学基金。

Olga Pochinka教授是常规动力系统理论和动力学中拓扑方法领域的领军人物之一。她在包括《Duke Math J》、《Selecta Mathematica》、《Izvestiya RAN》、《Survey in Math》、、《Results in Mathematics》、《Advances in Mathematics》等国际顶级数学和数学物理期刊上发表了100多篇论文，并撰写了关于动力系统理论的专著2部。

甘肃应用数学中心

甘肃省高校应用数学与复杂系统省级重点实验室

数学与统计学院

萃英学院

2024年8月27日