~amiloradovsky/symbolic-dynamics

symbolic-dynamics/ROADMAP.org -rw-r--r-- 1.2 KiB View raw
5857f238Andrew Miloradovsky .build.yml: continuous integration for SourceHut 7 months ago
                                                                                
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* Pierre's suggestions

- [-] reorganize modules (Topology, Uniform)
  - [ ] in Patterns: prove characterization of topology
  - [X] prove characterization of uniform continuity (=anchored local rules)
- [X] tidy a little (last section of Shifts.v ...)
- [ ] define shift homomorphisms, endomorphisms
  - [ ] their characterizations (=local rules)
- [ ] define SFT
  - [ ] define sofic (factors of SFT)
- [ ] define grouping
  - [ ] prove that it's a conjugacy
  - [ ] prove that SFT can be grouped into nearest-neighbor SFT
  - [ ] prove that sofic are symbolwise projections of nearest-neighbor SFT
- [ ] define substitutions over 1D words
  - [ ] extend them as continuous maps of A^ℕ and A^ℤ
  - [ ] prove it commutes with some shifts
- [ ] define rectangle substitutions over 2D words
  - [ ] extend them as continuous mpas of A^ℤ²
  - [ ] define S-adic (in 1D and 2D)

* Andrei's original

- [X] Uniform spaces and continuity
- [X] Shift spaces
- [X] Continuous maps

- [X] Group actions
- [X] Dynamical systems
- [ ] Topological entropy

- [ ] Directed multi- and hyper-graphs
- [ ] Free group-like structures on the alphabet
- [ ] Markov chains (1-d), stochastics?