Vershik, A. M.; Sidorov, N. A. Bijective coding of automorphisms of the torus and binary quadratic forms. (English. Russian original) Zbl 0934.37006 Russ. Math. Surv. 53, No. 5, 1106-1107 (1998); translation from Usp. Mat. Nauk. 53, No. 5, 231-232 (1998). The paper studies a certain class of maps from a symbolic compactum to a two-dimensional torus connecting a bidirectional translation with a given hyperbolic automorphism of a two-dimensional torus and preserving the maximum entropy measure. Known methods of geometric coding usually make use of the construction of so called Markov partitions, while the coding under consideration is constructed by means of the arithmetic and group theoretic structure. The latter makes it possible to connect the arithmetic of the corresponding algebraic extension with the dynamics of the automorphism. Reviewer: Michael L.Blank (Moskva) Cited in 1 Document MSC: 37A30 Ergodic theorems, spectral theory, Markov operators 28D05 Measure-preserving transformations 28D20 Entropy and other invariants 37A35 Entropy and other invariants, isomorphism, classification in ergodic theory 37B10 Symbolic dynamics 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) Keywords:homeomorphism; hyperbolicity; geometric coding; two-dimensional torus; hyperbolic automorphism; maximum entropy measure; Markov partitions PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{N. A. Sidorov}, Russ. Math. Surv. 53, No. 5, 1106--1107 (1998; Zbl 0934.37006); translation from Usp. Mat. Nauk. 53, No. 5, 231--232 (1998) Full Text: DOI