Map · 37
dynamical systems
MSC 37 · Dynamical systems and ergodic theory
955 declarations (821 theorems, 134 definitions) across 34 files. 0 of the 24 famous theorems listed for this area are in Mathlib (0%). 11 open conjectures here are stated in Lean.
Files are assigned to areas by a language model reading each file's documentation. Report a file that is in the wrong area.
Subareas4
- 37B Topological dynamics 623
- 37A Ergodic theory 178
- 37E Low-dimensional dynamical systems 145
- 37F Dynamical systems over complex numbers 9
Famous theorems0 of 24
From the 1000+ theorems project, which classifies each theorem by MSC area.
Not yet in Mathlib · 24
Open conjectures stated in Lean11
Statements without proofs, collected by the Formal Conjectures project.
- CollatzConjecture.collatz_conjectureWikipedia
- Erdos1135.erdos_1135Erdős Problems
- JugglerConjecture.juggler_conjectureWikipedia
- Mandelbrot.MLCWikipedia
- Mandelbrot.MLC_general_exponentWikipedia
- Mandelbrot.density_of_hyperbolicityWikipedia
Structures defined here6
Typeclasses defined in this area's files, most assumed first.
Files34
Largest first. The code after each file is its assigned subarea.
- Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber
Translation number of a monotone real map that commutes with `x ↦ x + 1`
37E · 145
- Mathlib.Dynamics.PeriodicPts.Defs
Periodic points
37B · 120
- Mathlib.Dynamics.SymbolicDynamics.Basic
Symbolic dynamics on cancellative monoids
37B · 81
- Mathlib.Dynamics.Flow
Flows and invariant sets
37B · 72
- Mathlib.Dynamics.TopologicalEntropy.CoverEntropy
Topological entropy via covers
37B · 56
- Mathlib.Logic.Function.Iterate
Iterations of a function
37B · 44
- Mathlib.Dynamics.TopologicalEntropy.NetEntropy
Topological entropy via nets
37B · 40
- Mathlib.Dynamics.Ergodic.Ergodic
Ergodic maps and measures
37A · 38
- Mathlib.Dynamics.OmegaLimit
ω-limits
37B · 38
- Mathlib.Dynamics.Ergodic.Action.OfMinimal
Ergodicity from minimality
37A · 28
- Mathlib.Dynamics.TopologicalEntropy.Subset
Topological entropy of subsets: monotonicity, closure, union
37B · 28
- Mathlib.Dynamics.Minimal
Minimal action of a group
37B · 26