Theorems · Definition · dynamical systems
Dynamics.coverEntropyEntourage
{X : Type u_1} → (X → X) → Set X → SetRel X X → ERealThe entropy of an entourage U, defined as the exponential rate of growth of the size
of the smallest (U, n)-refined cover of F. Takes values in the space of extended real numbers
[-∞, +∞]. This first version uses a limsup, and is chosen as the default definition.
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ERealstatement · cited by 793
- SetRelstatement and proof · cited by 581
- ENat.toENNRealproof · cited by 103
- ExpGrowth.expGrowthSupproof · cited by 42
- Dynamics.coverMincardproof · cited by 39
Cited by21
Results whose statement or proof uses this declaration.
- Dynamics.coverEntropyproof · cited by 22
- Dynamics.coverEntropyEntourage_antitonestatement · cited by 6
- Dynamics.coverEntropyInfEntourage_le_coverEntropyEntouragestatement · cited by 3
- Dynamics.coverEntropyEntourage_emptystatement · cited by 2
- Dynamics.coverEntropyEntourage_le_log_coverMincard_divstatement · cited by 2
- Dynamics.coverEntropyEntourage_monotonestatement · cited by 2
- Dynamics.le_coverEntropyEntourage_imagestatement · cited by 1
- Dynamics.coverEntropy_antitoneproof · cited by 1
- Dynamics.netEntropyEntourage_le_coverEntropyEntouragestatement · cited by 1
- Dynamics.coverEntropyEntourage_image_lestatement · cited by 1
- Dynamics.coverEntropy_unionproof · cited by 1
- Dynamics.coverEntropyEntourage_closurestatement · cited by 1