Topological dynamics | Entropy and information

Mean dimension

In mathematics, the mean (topological) dimension of a topological dynamical system is a non-negative extended real number that is a measure of the complexity of the system. Mean dimension was first introduced in 1999 by Gromov. Shortly after it was developed and studied systematically by Lindenstrauss and Weiss. In particular they proved the following key fact: a system with finite topological entropy has zero mean dimension. For various topological dynamical systems with infinite topological entropy, the mean dimension can be calculated or at least bounded from below and above. This allows mean dimension to be used to distinguish between systems with infinite topological entropy. Mean dimension is also related to the problem of embedding topological dynamical systems in shift spaces (over Euclidean cubes). (Wikipedia).

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Dimensions (1 of 3: The Traditional Definition - Directions)

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From playlist Exploring Mathematics: Fractals

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Dimensions Chapter 2

Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Dimensions Chapter 5

Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Dimensions Chapter 1

Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Dimensions Chapter 6

Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Dimensions Chapter 4

Chapter 4 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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From playlist Wolfram Physics Project Livestream Archive

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Wolfram Physics Project: Working Session Tuesday, Mar. 23, 2021 [Experimental Implications]

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From playlist Wolfram Physics Project Livestream Archive

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Linear Transformations -- Abstract Linear Algebra 13

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From playlist Abstract Linear Algebra

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Dimensional Analysis

We introduce the idea of dimensional analysis and its use in finding unknown quantities' dependence on relevant dimensionful variables.

From playlist Mathematical Physics I Uploads

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M2-branes and Supersymmetric Chern-Simons Theories, Part 1 - Daniel Jafferis

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From playlist PiTP 2010

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SHM - 16/01/15 - Constructivismes en mathématiques - Marie Françoise Roy

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From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques

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What do physicists mean by dimensions of space?

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From playlist Science Unplugged: Extra Dimensions

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Planarity in Higher Codimension Mean Curvature Flow - Keaton Naff

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From playlist Mathematics

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Xavier Ros-Oton: Regularity of free boundaries in obstacle problems, Lecture II

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From playlist Hausdorff School: Trending Tools

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Finding the Dimension of a Subspace

Description: How should we define the dimension of a subspace? In the past, we usually just point at planes and say duh its two dimensional. Here we give a precise definition, and use it to find the dimensions of the column space and null space of a matrix. Learning Objectives: 1) Define

From playlist Older Linear Algebra Videos

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Introduction Sphere Packing problems by Abhinav Kumar

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From playlist Sphere Packing - 2019

Related pages

Lebesgue covering dimension | Universal space | Mathematics | Metrizable space | Topological entropy