Ergodentheorie¶
Hopf, E. (1937). Ergodentheorie. Springer.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Ensemble
- Hopf's work
This sourceRigorous measure-theoretic ergodic theory formalising the convergence of time averages to ensemble averages (and applying ergodic methods to geodesic flows).
- Hopf's work
- Phase Space
- It licenses geometric and topological methods (Poincaré sections, bifurcation theory, KAM theorem, Lyapunov analysis), enables ensemble methods in statistical mechanics, and supports the quantum-classical correspondence via semiclassical phase-space methods.
This sourceDevelops rigorous measure-theoretic ergodic theory; formalizes Birkhoff's result in modern probability language; establishes that time averages converge to ensemble averages on measure-one sets; foundational for modern functional-analytic approach to ergodic theory.
- It licenses geometric and topological methods (Poincaré sections, bifurcation theory, KAM theorem, Lyapunov analysis), enables ensemble methods in statistical mechanics, and supports the quantum-classical correspondence via semiclassical phase-space methods.
Verification¶
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Registry ID ref:cd1190b13155 · see in the full table