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Self-Similar Sets and Measures on the Line

Offered By: International Mathematical Union via YouTube

Tags

Cantor Set Courses Fractal Geometry Courses

Course Description

Overview

Explore the fascinating world of fractal geometry in this 49-minute lecture on self-similar sets and measures on the line. Delve into central objects of interest, including classical examples like the Cantor set, SierpiƄski triangle, Koch snowflake curve, and Bernoulli convolutions. Examine the problem of determining the dimension of these objects, focusing on recent developments from the past four years. Learn about key concepts such as the Minkowski dimension, open set condition, dimension of measures, exponential separation condition, and algebraic parameters. Gain insights into proofs and mathematical techniques used in this field. Access accompanying slides for visual support and deeper understanding of the presented material.

Syllabus

Introduction
Definition
Commands
Bernoulli convolution
Minkowski dimension
Open set condition
Dimension of measures
Exponential separation condition
Algebraic parameters
Proofs


Taught by

International Mathematical Union

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