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.
Mobile