Index
Finite, toral, and Gaussian examples
Work from permutations to rotations and mixing maps, then transport cube dynamics into Gaussian coordinates.
Core idea
Work from permutations to rotations and mixing maps, then transport cube dynamics into Gaussian coordinates.
Prerequisite doorway
- Power set
- Indicator function
- Product measure
- Cumulative distribution function
- Orthogonal group
- Haar measure
- Fourier character on the standard torus
Reading path
- Symmetric group
- Cycle of a permutation
- Dynamics on a finite uniform probability space
- Fourier basis on a compact abelian group
- Rotation on a compact abelian group
- Ergodicity criterion for torus translations
- Doubling map of the circle
- Arnold cat map
- Bernoulli shift
- Standard Gaussian probability space
- Probability integral transform
- Linear Gaussian-preserving dynamics
- Gaussian dynamics by measurable conjugacy
- Ergodic Gaussian maps transported from rotations
Return to Ergodic theory.