Topological dynamics | Entropy and information
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).
Dimensions (1 of 3: The Traditional Definition - Directions)
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From playlist Exploring Mathematics: Fractals
Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 4 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
From playlist Dimensions Arabe/Arabic / العربية
Wolfram Physics Project: Working Session Tuesday, Apr. 20, 2021 [Dimension Decay]
This is a Wolfram Physics Project working session about dimension change in the early universe and dimension decay. Begins at 7:13 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the
From playlist Wolfram Physics Project Livestream Archive
Wolfram Physics Project: Working Session Tuesday, Mar. 23, 2021 [Experimental Implications]
This is a Wolfram Physics Project working session on experimental implications of physics models. Begins at 5:43 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post:
From playlist Wolfram Physics Project Livestream Archive
Linear Transformations -- Abstract Linear Algebra 13
⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.youtube.com/michaelpennmath non-math podcast: http
From playlist Abstract Linear Algebra
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
M2-branes and Supersymmetric Chern-Simons Theories, Part 1 - Daniel Jafferis
M2-branes and Supersymmetric Chern-Simons Theories, Part 1 Daniel Jafferis Institute for Advanced Study July 23, 2010
From playlist PiTP 2010
SHM - 16/01/15 - Constructivismes en mathématiques - Marie Françoise Roy
Marie-Françoise Roy (IRMAR, Université Rennes 1), « Méthodes constructives en algèbre abstraite : l'exemple de la dimension »
From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques
What do physicists mean by dimensions of space?
The 3 dimensions of our daily experience may be obvious, but a “dimension” means something specific to physicists. Brian Greene explains that meaning. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Fac
From playlist Science Unplugged: Extra Dimensions
Planarity in Higher Codimension Mean Curvature Flow - Keaton Naff
Analysis Seminar Topic: Planarity in Higher Codimension Mean Curvature Flow Speaker: Keaton Naff Affiliation: Columbia University Date: February 08, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Xavier Ros-Oton: Regularity of free boundaries in obstacle problems, Lecture II
Free boundary problems are those described by PDE that exhibit a priori unknown (free) interfaces or boundaries. Such type of problems appear in Physics, Geometry, Probability, Biology, or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations
From playlist Hausdorff School: Trending Tools
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
Introduction Sphere Packing problems by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019