Entropy and growth along orbits

Core idea

Entropy measures information in orbit observations. Subadditive and linear cocycles describe growth, leading to Kingman and Oseledets.

Prerequisite doorway

• Shannon entropy
• Linear map
• Regular representation

Reading path

• Subadditive cocycle
• Kingman subadditive ergodic theorem
• Linear cocycle over a dynamical system
• Lyapunov exponent of a linear cocycle
• Oseledets multiplicative ergodic theorem
• Finite measurable partition
• Kolmogorov–Sinai entropy
• Generating partition
• Kolmogorov–Sinai generator theorem
• Shannon–McMillan–Breiman theorem
• Koopman equivalence need not imply conjugacy

Return to Ergodic theory.