| 1. | The ergodic theorem has also had repercussions for dynamics.
|
| 2. | The multiplicative ergodic theorem is stated in terms of matrix cocycles of a dynamical system.
|
| 3. | Kingman's subadditive ergodic theorem can be used to prove statements about Lyapunov exponents.
|
| 4. | In the 1930s, independently of John von Neumann, he discovered the mean ergodic theorem.
|
| 5. | A conceptually different proof of the multiplicative ergodic theorem was found by M . S . Raghunathan.
|
| 6. | This shows the possibility of serious errors when using the ergodic theorem for the study of physical systems.
|
| 7. | Birkhoff's most durable result has been his 1931 discovery of what is now called the ergodic theorem.
|
| 8. | The ergodic theorem has also had repercussions for dynamics, probability theory, group theory, and functional analysis.
|
| 9. | Overisel is the birthplace of mathematician George David Birkhoff, best known for what is now called the ergodic theorem.
|
| 10. | Quantum ergodic theorem originated by John von Neumann is a strong result arising from the mere mathematical structure of quantum mechanics.
|
