A lemniscate in complex analysis isn’t one fixed shape. It’s any level set of |p(z)|. So we study |p(z)| = c As you vary c, the curve can split into multiple loops, fuse together, or pinch off entirely. Those structural changes tend to organize around points where p′(z)=0. #ComplexAnalysis #Polynomials #ComplexDynamics #Lemniscates #MathArt

You are watching the dance of Critical Points and Lemniscates in a 24-Root Complex Polynomial. In complex analysis, lemniscate is the general object not just a figure-8, but any level set of the modulus. For a complex polynomial p(z), a lemniscate is the curve |p(z)| = c, so it can split into many closed loops, merge, pinch, and reshape as c moves often at values tied to critical points (where p′(z)=0). #ComplexAnalysis #Polynomials #ComplexDynamics #CriticalPoints #Lemniscates #MathArt

Prof. Sabyasachi Mukherjee, School of Mathematics, @TIFRScience, received the Infosys Prize 2025 in Mathematical Sciences for his groundbreaking work linking the dynamics of Kleinian group actions and complex dynamics. #TIFR #InfosysPrize #Mathematics #ComplexDynamics

#AwardAlert Prof. Anjana Badrinarayanan (NCBS-TIFR, Bengaluru) and Prof. Sabyasachi Mukherjee (TIFR, Mumbai) have been awarded the Infosys Prize 2025 in Life Sciences and Mathematical Sciences, respectively. #TIFRScience #InfosysPrize #Mathematics #ComplexDynamics

The Infosys Prize 2025 in Mathematical Sciences is awarded to Prof. Sabyasachi Mukherjee, Associate Professor at the Tata Institute of Fundamental Research, Mumbai. His work links different areas of mathematics, such as group dynamics and complex analysis, to study patterns that emerge from simple rules. Prof. Mukherjee’s research reflects both the creativity and precision at the heart of mathematical thought. @TIFRScience #infosysprize #infosyssciencefoundation #mathematics #complexdynamics #TIFR #researchexcellence #innovation

List X about List Y, Algorithm Z, SigmaXyzwmxn Complexdynamics Planets, Strategical Sums²📊🫧❤️🪐 @xai @grok @threejs @clcoding

List X about List Y, Algorithm Z, SigmaXyzwmxn Complexdynamics Planets, Strategical Sums¹📊🫧❤️🪐 @xai @grok @threejs @grok

List X about List Y, Algorithm Z, SigmaXyzwmxn Complexdynamics Planets, Heat Map📊🫧❤️🪐 @xai @grok @threejs @grok

#mdpisymmetry Check this published article "Dynamics of Iterations of the Newton Map of sin(z)" at brnw.ch/21wQQJ8 Authors: Aimée Cloutier et al. #complexdynamics #trigonometricfunctions @RoseHulman @OleMiss @TexasTech @newmexicotech (IOAP Member)

🆕🎬Arithmetic, Algebraic and Analytics Dynamics Luo, Yusheng (2025). Degeneration of rational maps and hyperbolic components - Lecture 1-2-3. CIRM. Audiovisual resource dx.doi.org/10.24350/CIRM.V.2… dx.doi.org/10.24350/CIRM.V.2… dx.doi.org/10.24350/CIRM.V.2… @_CIRM #Maths #ComplexDynamics

Free to read: KCC theory for a type of nonlinear damped SD oscillators. This paper applies #KCCtheory to study smooth and #discontinuousoscillators, highlighting distinct #geometricproperties and #complexdynamics from small parameter changes.

Great new work by Jian-Guo Wang et al @XJTU1896 - 'JefiAtten: an attention-based #neuralnetwork model for solving #Maxwell's #equations with charge and current sources' - iopscience.iop.org/article/1… #machinelearning #plasmas #compphys #PINNs #complexdynamics #simulation #AI

💢در آخرین مصاحبه خود با الشرق نیوز، من این امتیاز را داشتم که نماینده ITSS Verona باشم و به تفاوت های ظریف بین واکنش های آمریکا و اروپا به حوثی ها در دریای سرخ پرداختم. 🌊 #ژئوپلیتیک #امنیت در حالی که واکنش ایالات متحده بر اساس رویکردی چند لایه عمل می کند که با اقدام قاطعانه مشخص می شود، موضع اروپا به سمت اقدامات دفاعی متمایل است و بر حفاظت از کشتی های اروپایی در حال تردد در دریای سرخ تأکید دارد. 🇺🇸🇪🇺 #واکنش_آمریکا #واکنش_اروپا استراتژی ایالات متحده در چهار سطح متمایز آشکار می شود: اول، اختلال در تدارکات. دوم، هدف قرار دادن سایت های نظامی. سوم، اعمال فشار اقتصادی از طریق تخریب تسهیلات صادراتی. و در نهایت، هدف قرار دادن رهبران سیاسی گروه های تروریستی نیابتی. 📉💥 #استراتژی_آمریکا #حوثی در مقابل، رویکرد اروپایی حفظ منافع دریایی، تعهد اقدامات دفاعی و در عین حال آماده ماندن برای دفاع از دارایی های اروپایی در صورت لزوم، البته با هزینه های قابل توجه در صورت لزوم، اولویت دارد. ⚔️💼 #اروپایی #امنیت_دریایی #اقدام_دفاعی این دوگانگی بر پویایی پیچیده شکل‌دهنده پاسخ‌های بین‌المللی به درگیری‌های منطقه‌ای تأکید می‌کند و دیدگاه‌ها و استراتژی‌های متفاوتی را برای رسیدگی به چالش‌های امنیتی در منطقه دریای سرخ برجسته می‌کند. 🌍🔍 #امنیت_منطقه #ComplexDynamics #RedSeaConflict

🇺🇸The U.S. veto in the UN Security Council shows unwavering support for "Israel's right to defend itself” against Hamas terror. Understanding the complexity of Gaza's situation, this decision reflects America's stance on the matter. 🌍🕊️ #IStandWithIsrael #ComplexDynamics

This article is about complex Dynamics Systems Turbulence Flow in Fluid Mechanics mathematical model and analysis method. #Chaos #ComplexDynamics #education #Engineering #FluidsMechanics #Turbulence #TurbulenceFlow #University #engineer #article tunavatansever.com/2021/03/0…

Today, we kicked off our Spring MACSI Seminar Series with #BenGoddard from the @EdinburghUni with his talk: Bounded Confidence Models of Opinion Dynamics. #complexdynamics #phasetransitions #boundaryconditions #radicals #externalpotential #springseminarseriesMACSI

Today Gustavo Ferreira (@OUMathsStats) came to Liverpool to give a talk about his recent results on multiply connected #wanderingdomains at our Dynamical Systems seminar! #complexdynamics

Today I gave a talk at the #CAvid seminar! You can find the recording and the slides here: mediacentral.ucl.ac.uk/Play/… #complexdynamics #wanderingdomains

New #SpecialIssue "Quantum Computing for Complex Dynamics", edited by Prof. Dr. GuiLu Long, Dr. Shijie Wei and Prof. Dr. Heng Fan, deadline 30 June 20. Look forward to your submissions! mdpi.com/journal/entropy/spe… #quantumcomputing #quatumalgorithms #complexdynamics #quantumchaos

Today @LasseRempe and I started an online mini-course on "Boundaries of Wandering Domains - topology and dynamics" at the RIMS Workshop on #ComplexDynamics @univkyoto (slides available at sites.google.com/view/rims-c…). Next talk is tomorrow at 7am UK time on wandering Lakes of Wada!