1983/01/10 by David Chernoff, John D. Barrow · 3 citations
Mathematics · Economics, Econometrics and Finance · #advanced mathematical theories #Mathematical Dynamics and Fractals #Complex Systems and Time Series Analysis #Ergodic theory #Physics #Chaotic #Nonlinear system #Invariant (physics) #Statistical physics #Classical mechanics #Entropy (arrow of time) #Mixing (physics) #Theoretical physics #Mathematical physics #Quantum mechanics #Mathematical analysis #Mathematics
paper · doi:10.1103/physrevlett.50.134
openalex publication_date 1983/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/03
A four-dimensional system of nonlinear difference equations describing the evolution of the general relativistic "mixmaster" cosmological model is studied. The evolution splits into two parts: one given by a (chaotic) generalized Baker's transformation and the other by a (systematic) change of scales. The chaotic degrees of freedom are studied in detail: Their evolution may be described by a two-sided shift and the invariant measure for these variables is found. Strong ergodic properties (mixing, nonzero entropy) are deduced.