| [1] |
J. Aaronson, An Introduction to Infinite Ergodic Theory, American Mathematical Society, Providence, RI, 1997. · Zbl 0882.28013 |
| [2] |
R. L. Adler, f -expansions revisited, in Recent Advances in Topological Dynamics, 318, Springer LNM, 1973, 1-5. · Zbl 0257.28012 |
| [3] |
R. L. Adler, A selection of problems in topological and symbolic dynamics, in Lecture Notes in Math., 729, Springer-Verlag, Berlin, Heidelherg, New York, 1979, 8-12. · Zbl 0424.54034 |
| [4] |
R. L. Adler, The torus and the disk, IBM J. Res. & Dev., 13, 224-234 (1987) · doi:10.1147/rd.312.0224 |
| [5] |
R. L. Adler; D. Coppersmith; M. Hassner, Algorithms for sliding block codes - an application of symbolic dynamics to information theory, IEEE Trans. Inform. Theory, 29, 5-22 (1983) · Zbl 0499.94009 · doi:10.1109/TIT.1983.1056597 |
| [6] |
R. L. Adler; J.-P. Dedieu; J. Y. Margulies; M. Martens; M. Shub, Newton’s method on Riemannian manifolds and a geometric model for the human spine, IMA J. Numerical Analysis, 22, 359-390 (2002) · Zbl 1056.92002 · doi:10.1093/imanum/22.3.359 |
| [7] |
R. L. Adler; L. Flatto, Geodesic flows, interval maps, and symbolic dynamics, Bull. Amer. Math. Soc., 25, 229-334 (1991) · Zbl 0802.58037 · doi:10.1090/S0273-0979-1991-16076-3 |
| [8] |
R. L. Adler; W. Goodwyn; B. Weiss, Equivalence of topological shifts, Israel J. Math, 27, 48-63 (1977) · Zbl 0362.54034 · doi:10.1007/BF02761605 |
| [9] |
R. L. Adler, M. Hassner and J. P. Moussouris, Method and Apparatus for Generating a Noiseless Sliding Block Code for a (1, 7) Channel with Rate 2/3, United States Patent 4,413,251. November 1, 1983. |
| [10] |
R. L. Adler; A. G. Konheim; M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc., 114, 309-319 (1965) · Zbl 0127.13102 · doi:10.1090/S0002-9947-1965-0175106-9 |
| [11] |
R. L. Adler; B. P. Kitchens; M. Martens; C. P. Tresser; C. W. Wu, The mathematics of halftoning, IBM J. Res. & Dev., 27, 5-15 (2003) · doi:10.1147/rd.471.0005 |
| [12] |
R. L. Adler; B. P. Kitchens; M. Martens; C. Pugh; M. Shub; C. P. Tresser, Convex dynamics and applications, Erg. Theory & Dynam. Sys., 25, 321-352 (2005) · Zbl 1076.37537 · doi:10.1017/S0143385704000537 |
| [13] |
R. L. Adler and B. Marcus, Topological entropy and equivalence of dynamical systems, Mem. Amer. Math. Soc., 20 (1979), iv+84 pp. · Zbl 0412.54050 |
| [14] |
R. L. Adler; T. Nowicki; G. Swirszcz; C. P. Tresser; S. Winograd, Error diffusion on acute simplices: Invariant tiles, Israel J. Math., 221, 445-469 (2017) · Zbl 1377.37026 · doi:10.1007/s11856-017-1550-7 |
| [15] |
R. L. Adler; R. Palais, Homeomorphic conjugacy of automorphisms on the torus, Proc. Amer. Math. Soc., 16, 1222-1225 (1965) · Zbl 0229.22013 · doi:10.1090/S0002-9939-1965-0193181-8 |
| [16] |
R. L. Adler, Symbolic dynamics and Markov partitions, Bull. Amer. Math. Soc. (N.S.), 35, 1-56 (1998) · Zbl 0892.58019 · doi:10.1090/S0273-0979-98-00737-X |
| [17] |
R. L. Adler; B. Weiss, Entropy, a complete metric invariant for automorphisms of the torus, Proc. Nat. Acad. Sci. U.S.A., 57, 1573-1576 (1967) · Zbl 0177.08002 · doi:10.1073/pnas.57.6.1573 |
| [18] |
R. L. Adler; B. Weiss, The ergodic infinite measure preserving transformation of Boole, Israel J. Math., 16, 263-278 (1973) · Zbl 0298.28012 · doi:10.1007/BF02756706 |
| [19] |
J. Ashley, G. Jaquette, B. Marcus and P. Seger, Runlength Limited Encoding/Decoding with Robust Resync, US Patent 5969649. |
| [20] |
A. Barbero; E. Rosnes; G. Yang; O. Ytrehus, Near-field passive RFID communication: Channel model and code design, IEEE Trans. Communications, 62, 1716-1726 (2014) |
| [21] |
K. Berg, On the Conjugacy Problem for K-Systems, Ph.D. thesis, University of Minnesota, 1967. |
| [22] |
R. Bowen, Markov partitions for Axiom A diffeomorphisms, American Journal of Mathematics, 92, 725-747 (1970) · Zbl 0208.25901 · doi:10.2307/2373370 |
| [23] |
R. Bowen, Topological entropy for noncompact sets, Transactions of the AMS, 184, 125-136 (1973) · Zbl 0274.54030 · doi:10.1090/S0002-9947-1973-0338317-X |
| [24] |
M. Boyle; J. Buzzi, The almost Borel structure of surface diffeomorphisms, Markov shifts and their factors, JEMS, 19, 2739-2782 (2017) · Zbl 1377.37017 · doi:10.4171/JEMS/727 |
| [25] |
M. Coornaert, Topological Dimension and Dynamical Systems, Springer, Universitext, 2015. · Zbl 1326.54001 |
| [26] |
O. Elishco; T. Meyerovitch; M. Schwartz, On encoding semiconstrained systems, IEEE Trans. Inform. Theory, 64, 2474-2484 (2018) · Zbl 1390.94677 · doi:10.1109/TIT.2017.2771743 |
| [27] |
E. I. Dinaburg, On the relations among various entropy characteristics of dynamical systems, Math USSR Isvestia, 5, 337-378 (1971) · Zbl 0248.58007 |
| [28] |
T. N. T. Goodman, Relating topological entropy and measure entropy, Bull. London Math. Soc., 3, 176-180 (1971) · Zbl 0219.54037 · doi:10.1112/blms/3.2.176 |
| [29] |
L. W. Goodwyn, Topological entropy bounds measure-theoretic entropy, Proceedings AMS, 23, 679-688 (1969) · Zbl 0186.09804 · doi:10.1090/S0002-9939-1969-0247030-3 |
| [30] |
M. Hochman, Isomorphism and embedding of Borel systems on full sets, Acta Appl. Math., 126, 187-201 (2013) · Zbl 1339.37007 · doi:10.1007/s10440-013-9813-8 |
| [31] |
K. A. S. Immink, EFMPlus, 8-16 Modulation Code, US Patent 5696505. |
| [32] |
K. A. S. Immink, Codes for Mass Data Storage Systems, 2nd edition, Shannon Foundation Publishers, 2004. |
| [33] |
A. N. Kolmogorov, New metric invariants of transitive dynamical systems and automorphisms of Lebesgue spaces, Dokl. Akad. Nauk SSSR, 119, 861-864 (1958) · Zbl 0083.10602 |
| [34] |
B. Marcus, Factors and extensions of full shifts, Monats. Math., 82, 239-247 (1979) · Zbl 0432.54036 · doi:10.1007/BF01295238 |
| [35] |
B. Marcus, The impact of Roy Adler’s work on symbolic dynamics and applications to data storage, in Symbolic Dynamics and Its Applications (New Haven, CT, 1991), Contemporary Mathematics, 135, Amer. Math. Soc., Providence, RI, 1992, 33-56. · Zbl 0784.54041 |
| [36] |
W. Parry, Intrinsic Markov chains, Trans. AMS, 112, 55-66 (1964) · Zbl 0127.35301 · doi:10.1090/S0002-9947-1964-0161372-1 |
| [37] |
W. Parry, A finitary classification of topological Markov chains and sofic shifts, Bull. LMS, 9, 86-92 (1977) · Zbl 0352.60054 · doi:10.1112/blms/9.1.86 |
| [38] |
Y. B. Pesin, Dimension Theory in Dynamical Systems, Chicago Lectures in Mathematics University of Chicago Press, Chicago, IL 1997. |
| [39] |
M. Ratner, On Raghunathan’s measure conjecture, Ann. of Math., 134, 545-607 (1991) · Zbl 0763.28012 · doi:10.2307/2944357 |
| [40] |
R. Roth; P. Siegel, On parity-preserving constrained coding, Procedings of the International Symposium in Information Theory, 1804-1808 (2018) |
| [41] |
O. Sarig, Symbolic dynamics for surface diffeomorphisms with positive entropy, Journal of the AMS, 26, 341-426 (2013) · Zbl 1280.37031 · doi:10.1090/S0894-0347-2012-00758-9 |
| [42] |
C. Shannon, A mathematical theory of communication, Bell. Sys. Tech. J., 27, 379-423,623-656 (1948) · Zbl 1154.94303 · doi:10.1002/j.1538-7305.1948.tb01338.x |
| [43] |
J. G. Sinai, Markov partitions and \(U\)-diffeomorphisms, Funkcional. Anal. i Prilozen, 2, 64-89 (1968) · Zbl 0182.55003 |
| [44] |
A. N. Trahtman, The road coloring problem, Israel J. Math., 172, 51-60 (2009) · Zbl 1175.05058 · doi:10.1007/s11856-009-0062-5 |
| [45] |
B. Weiss, On the work of Roy Adler in ergodic theory and dynamical systems, in Symbolic Dynamics and Its Applications (New Haven, CT, 1991), Contemporary Mathematics, 135, Amer. Math. Soc., Providence, RI, 1992, 19-32. · Zbl 0776.28010 |
| [46] |
R. F. Williams, Classification of subshifts of finite type, Annals of Math., 98 (1973), 120-153; Erratum, 99 (1974), 380-381. · Zbl 0282.58008 |
