Chaotic maps

Complex squaring map

In mathematics, the complex squaring map, a polynomial mapping of degree two, is a simple and accessible demonstration of chaos in dynamical systems. It can be constructed by performing the following steps: 1. * Choose any complex number on the unit circle whose argument (angle) is not a rational multiple of π, 2. * Repeatedly square that number. This repetition (iteration) produces a sequence of complex numbers that can be described alone by their arguments. Any choice of starting angle that satisfies (1) above will produce an extremely complicated sequence of angles, that belies the simplicity of the steps. It can be shown that the sequence will be chaotic, i.e. it is sensitive to the detailed choice of starting angle. (Wikipedia).

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Dividing Complex Numbers Example

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From playlist Complex Numbers

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Complex Numbers in Trigonometric Form

This video explains how to write complex numbers in trigonometric form. http://mathispower4u.wordpress.com/

From playlist Complex Numbers

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Visualizing simple complex functions -- Complex Analysis 3

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From playlist Complex Analysis

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Digression: The cotangent complex and obstruction theory

We study the cotangent complex more in depth and explain its relation to obstruction theory. As an example we construct the Witt vectors of a perfect ring. This video is a slight digression from the rest of the lecture course and could be skipped. Feel free to post comments and questions

From playlist Topological Cyclic Homology

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Duality In Higher Categories II by Pranav Pandit

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

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Part I: Complex Variables, Lec 3: Conformal Mappings

Part I: Complex Variables, Lecture 3: Conformal Mappings Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT Calculus Revisited: Calculus of Complex Variables

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Higher algebra 4: Derived categories as ∞-categories

In this video, we construct the ∞-categorical refinement of the derived category of an abelian category. This is the fourth video in our introduction to ∞-categories and Higher Algebra. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA

From playlist Higher Algebra

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L^2 geometry of moduli spaces of vortices and lumps (Lecture 1) by James Martin Speight

PROGRAM VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual field the

From playlist Vortex Moduli - 2023

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Mod-02 Lec-19 Special Techniques III

Electromagnetic Theory by Prof. D.K. Ghosh,Department of Physics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist IIT Bombay: Electromagnetic Theory

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Complex Analysis - Part 5 - Total Differentiability in ℝ²

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From playlist Complex Analysis

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Graphs in the Complex Plane (1 of 3: Perpendicular bisector - visual method)

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From playlist Using Complex Numbers

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Part I: Complex Variables, Lec 2: Functions of a Complex Variable

Part I: Complex Variables, Lecture 2: Functions of a Complex Variable Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT Calculus Revisited: Calculus of Complex Variables

Related pages

Orbit (dynamics) | Radian | Logistic map | Polynomial | Complex number | Natural number | Mathematics | Rational number | Dynamical system | Quadratic function | Unit circle | Chaos theory | Sequence | Degree of a polynomial | Dyadic transformation | Euler's formula