报告题目1：On convergence of normal form transformations

报告人：Valery Romanovski教授，University of Maribor

报告时间：2026年9月17日（周四）8:20-9:20

报告地点：20-308

报告摘要：We discuss some aspects concerning transformations of local analytic, or formal vector fields to Poincare-Dulac normal form, and the convergence of such transformations. We first mention A.D. Bruno's approach to formal normalization, as well as convergence results in presence of certain (simplified) versions of Bruno's “Condition A'”, and along the way we also identify a large class of systems that satisfy Bruno's diophantine “Condition omega”. We then introduce a new formalism that allows essentially simplify the proof of convergence.  We also show how Bruno's approach naturally extends to an elementary proof of L. Stolovitch's formal and analytic simultaneous normalization theorems for abelian Lie algebras of vector fields.

The talk is based on the recent work:

[1] T. Petek, V. G. Romanovski, On computations of Poincare-Dulac normal forms,

J. Differential Equations,  452, 113781 (2026).

[2] V. G. Romanovski, S. Walcher,Poincarè-Dulac Normal Forms: Formal and Analytic Aspects, https://arxiv.org/abs/2510.00925

报告人简介：Valery Romanovski studied mathematics at the Faculty of Mathematics and Mechanics ofLeningrad State University (USSR).In 1983 he received his diploma and in 1986 his PhD degree from the university. From 1987 to 1990he worked as anAssistant Professor at theBranch of Moscow Aviation Institute at Baikhonur Space Center. Then he moved to Minsk to work at the Belarusian State University for Informatics and Radioelectronics. In 2001 he defended his habilitation thesis and was awarded the degreeDoctor of Physical and Mathematical Sciences (the highest scientific degree in some countries of former USSR) from theInstituteof Mathematics of National Academy of Science of Belarus. From the year 2000 he is permanently employed as a researcher at the Center for Applied Mathematics and Theoretical Physics of the University Maribor (Slovenia). In the year 2014 he was elected as a full professor of mathematics at the University of Maribor. At present he teaches a few mathematical courses at the Faculty of Natural Sciences and theFaculty of Electrical Engineering and Computer Science, of the University of Maribor. For short periods (1-9 months) he was a visiting professor at the University of North Carolina at Charlotte, al Farabi Kazakh National University, al Farabi Kazakh National University, and delivered short lecture courses at RWTH Aachen University, University of Sao Paolo, Grodno State University. For years 2012-2016 he was appointed asDistinguished Professor of Shanghai Normal University. Six young researchers have successfully completed PhD studies under hissupervision/co-supervision. His research works are related to the theory of dynamical systems, computational algebra,andapplications to biochemical networks. He is author/co-author of about150 research articles published in leading international journals anda co-author ofresearch monograph published by Birkhauser. He is a member of Editorial Boards ofJournal of Applied Analysis and Computation, Mathematics,and Qualitative Theory of Dynamical Systems.

报告题目2：On spectral theory of singular Hamiltonian systems

报告人：沈建和教授，福建师范大学

报告时间：2026年9月17日（周四）9:20-10:20

报告地点：20-308

报告摘要：In this paper, we extend the pushed-to-pulled transition theory to the Keller-Segel model with saturation term based on geometric singular perturbation theory. In the current setting with saturation term, the explicit closed-form expressions for the transition coefficient are now unavailable. We resolve this problem via the mass-frame adjoint formulation, deriving the exact far-field asymptotic limit of the adjoint zero mode and eliminating far-field quadrature. This yields the full pushed-to-pulled transition boundary and sharp wave-speed selection criteria for the current saturated situation.

报告人简介：沈建和，福建师范大学数学与统计学院教授、博士生导师、副院长，兼任中国数学会奇异摄动专业委员会副主任、福建省数学会秘书长和福建省生物数学学会会长，美国《数学评论》和德国《数学文摘》评论员等；研究方向为奇异摄动理论及应用；已在《Philosophical Transactions of the Royal Society A》、《Journal of Differential Equations》、《European Journal of Applied Mathematics》、《Studies in Applied Mathematics》、《Physica D: Nonlinear Phenomenon》、《Chaos》、《Journal of Dynamics and Differential Equations》、《Discrete and Continuous Dynamical Systems》等杂志发表论文约30篇；主持或主持完成国家自然科学基金面上项目和青年项目3项、福建省自然科学基金重点项目和面上项目各1项等；入选百千万人才工程省级人选（2019年）和福建省雏鹰计划青年拔尖人才计划（2020年）等。

报告题目3：Small limit cycles produced in piecewise smooth near-integrable systems

报告人：田云教授，上海师范大学

报告时间：2026年9月17日（周四）10:20-11:20

报告地点：20-308

报告摘要：In this talk, we consider Hopf bifurcation of small-amplitude limit cycles near a center in polynomial near-integrable systems under piecewise smooth perturbations. The methods of Lyapunov constants and asymptotic expansions of Melnikov functions are applied to get new lower bounds on the maximal number of small-amplitude limit cycles produced by Hopf bifurcation in such quadratic and cubic systems.

报告人简介：田云，加拿大西安大略大学应用数学博士，现为上海师范大学数理学院教授，博士生导师，主要从事微分方程定性理论、计算机符号计算和传染病模型等方向的研究，特别关注弱化的Hilbert第16问题、同宿异宿极限环分支和规范型的符号计算等相关问题。近年来，在JDE、Commun. Nonl. Sci. Numer. Simul、Nonlinear Anal. RWA等本领域主流期刊发表学术论文30余篇。

报告题目4：High frequency instability of small-amplitude periodictraveling waves in a generalized Dullin–Gottwald–Holmequation

报告人：孙宪波教授，杭州师范大学

报告时间：2026年9月17日（周四）11:20-12:20

报告地点：20-308

报告摘要：This paper investigates the spectral stability of small-amplitude periodic traveling wave solutionsto a generalized Dullin–Gottwald–Holm (DGH) equation incorporating a third-order lineardispersive term γuxxx. While the modulational instability of such waves is well-understoodnear the spectral origin, our analysis focuses on the more robust high-frequency instabilities(HFIs) arising from resonant mode collisions away from the origin. By employing a Lyapunov-Schmidt reduction, we first establish the existence of a one-parameter family of smooth periodicwave profiles bifurcating from the trivial solution. Within the framework of Floquet-Bloch

theory, we demonstrate that the inclusion of the linear dispersion coefficient γ fundamentallyreconfigures the resonance locus, triggering the collision of purely imaginary eigenvalues withopposite Krein signatures. A rigorous perturbation analysis on the critical eigenspaces is performedto derive the analytical criteria for the onset of HFI.We show that the instability regionsare intricately determined by the nonlinear parameter b, the wavenumber k, and the dispersioncoefficient γ, revealing a complex spectral landscape where high-frequency modes can becomeunstable even when the wave is modulationally stable.

报告人简介：孙宪波，杭州师范大学教授，博士生导师。研究方向为微分方程定性理论及其应用，在JDE，SCM，DCDS B，JSC，BSM等国际主流SCI期刊上发表学术论文四十余篇，主持4项国家自然科学基金，省部级项目3项。

邀请人：动力系统与非线性分析研究所