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Papers authored by William Parry [1] Parry, W.. On the β-expansions of real numbers. Acta Math. Acad. Sci. Hungar. 11 (1960), 401–416. [2] Parry, W.. Ergodic properties of some permutation processes. Biometrika 49 (1962), 151–154. [3] Kakutani, S. and Parry, W.. Infinite measure preserving transformations with mixing. Bull. Amer. Math. Soc. 69 (1963), 752–756. [4] Parry, W.. An ergodic theorem of information theory without invariant measure. Proc. London Math. Soc. 13(3) (1963), 605–612. [5] Parry, W.. Intrinsic Markov chains. Trans. Amer. Math. Soc. 112 (1964), 55–66. [6] Parry, W.. On Rohlin’s formula for entropy. Acta Math. Acad. Sci. Hungar. 15 (1964), 107–113. [7] Parry, W.. Note on the ergodic theorem of Hurewicz. J. London Math. Soc. 39 (1964), 202–210. [8] Parry, W.. Representations for real numbers. Acta Math. Acad. Sci. Hungar. 15 (1964), 95–105. [9] Hahn, F. and Parry, W.. Minimal dynamical systems with quasi-discrete spectrum. J. London Math. Soc. 40 (1965), 309–323. [10] Parry, W.. Ergodic and spectral analysis of certain infinite measure preserving transformations. Proc. Amer. Math. Soc. 16 (1965), 960–966. [11] Hoare, H. and Parry, W.. Affine transformations with quasi-discrete spectrum. I. J. London Math. Soc. 41 (1966), 88–96. [12] Parry, W.. Generators and strong generators in ergodic theory. Bull. Amer. Math. Soc. 72 (1966), 294–296. [13] Hoare, H. and Parry, W.. Affine transformations with quasi-discrete spectrum. II. J. London Math. Soc. 41 (1966), 529–530. [14] Parry, W.. Symbolic dynamics and transformations of the unit interval. Trans. Amer. Math. Soc. 122 (1966), 368–378. [15] Parry, W.. On the coincidence of three invariant σ-algebras associated with an affine transformation. Proc. Amer. Math. Soc. 17 (1966), 1297–1302. [16] Hoare, H. and Parry, W.. Semi-groups of affine transformations. Quart. J. Math. Oxford Ser. (2) 17 (1966), 106–111. [17] Newton, D. and Parry, W.. On a factor automorphism of a normal dynamical system. Ann. Math. Statist. 37 (1966), 1528–1533. [18] Laxton, R. and Parry, W.. On the periodic points of certain automorphisms and a system of polynomial identities. J. Algebra 6 (1967), 388–393. [19] Parry, W.. Principal partitions and generators. Bull. Amer. Math. Soc. 73 (1967), 307–309. [20] Parry, W.. Generators for perfect partitions. Dokl. Akad. Nauk SSSR 173 (1967), 264–266. [21] Parry, W.. Aperiodic transformations and generators. J. London Math. Soc. 43 (1968), 191–194. [22] Hahn, F. and Parry, W.. Some characteristic properties of dynamical systems with quasi-discrete spectra. Math. Systems Theory 2 (1968), 179–190. [23] Parry, W.. Zero entropy of distal and related transformations. Topological Dynamics (Symposium, Colorado State University, Fort Collins, CO, 1967). Eds. J. Auslander and W. H. Gottschalk. Benjamin, New York, 1968, pp. 383–389. [24] Parry, W.. Ergodic properties of affine transformations and flows on nilmanifolds. Amer. J. Math. 91 (1969), 757–771. [25] Parry, W.. Compact abelian group extensions of discrete dynamical systems. Z. Wahrsch. Verw. Gebiete 13 (1969), 95–113. [26] Parry, W.. Entropy and Generators in Ergodic Theory. W. A. Benjamin, New York, 1969. [27] Parry, W.. Spectral analysis of G-extensions of dynamical systems. Topology 9 (1970), 217–224. [28] Parry, W.. Dynamical systems on nilmanifolds. Bull. London Math. Soc. 2 (1970), 37–40. [29] Parry, W. and Walters, P.. Minimal skew-product homeomorphisms and coalescence. Compos. Math. 22 (1970), 283–288. [30] Parry, W.. Metric classification of ergodic nilflows and unipotent affines. Amer. J. Math. 93 (1971), 819–828. [31] Parry, W.. Ergodic theory of G-spaces. Actes du Congrès International des Mathématiciens (Nice, 1970, Tome 2). Gauthier-Villars, Paris, 1971, pp. 921–924. [32] Parry, W. and Walters, P.. Endomorphisms of a Lebesgue space. Bull. Amer. Math. Soc. 78 (1972), 272–276. Also: Erratum to ‘Endomorphisms of a Lebesgue space’. Bull. Amer. Math. Soc. 78 (1972), 628. [33] Azencott, R. and Parry, W.. Stability of group representations and Haar spectrum. Trans. Amer. Math. Soc. 172 (1972), 317–327. [34] Parry, W.. Cocycles and velocity changes. J. London Math. Soc. 5(2) (1972), 511–516. [35] Jones, R. and Parry, W.. Compact abelian group extensions of dynamical systems. II. Compos. Math. 25 (1972), 135–147. [36] Parry, W.. Dynamical representations in nilmanifolds. Compos. Math. 26 (1973), 159–174. [37] Parry, W.. Notes on a posthumous paper by F. Hahn. Israel J. Math. 16 (1973), 38–45. [38] Parry, W.. Class properties of dynamical systems. Recent Advances in Topological Dynamics (Proc. Conf., Yale University, New Haven, CT, 1972; in honor of Gustav Arnold Hedlund) (Lecture Notes in Mathematics, 318). Springer, Berlin, 1973, pp. 218–225. [39] Parry, W.. A note on cocycles in ergodic theory. Compos. Math. 28 (1974), 343–350. [40] Fellgett, R. and Parry, W.. Endomorphisms of a Lebesgue space. II. Bull. London Math. Soc. 7 (1975), 151–158. [41] Parry, W.. Endomorphisms of a Lebesgue space. III. Conference on Ergodic Theory and Topological Dynamics (Kibbutz Lavi, 1974). Israel J. Math. 21 (1975), 167–172. [42] Parry, W. and Sullivan, D.. A topological invariant of flows on 1-dimensional spaces. Topology 14 (1975), 297–299. [43] Parry, W. and Schmidt, K.. A note on cocycles of unitary representations. Proc. Amer. Math. Soc. 55 (1976), 185–190. [44] Parry, W.. Some classification problems in ergodic theory. Sankhyā Ser. A 38 (1976), 38–43. [45] Parry, W. and Williams, R.. Block coding and a zeta function for finite Markov chains. Proc. London Math. Soc. (3) 35 (1977), 483–495. [46] Parry, W.. A finitary classification of topological Markov chains and sofic systems. Bull. London Math. Soc. 9 (1977), 86–92. [47] Parry, W.. The information cocycle and ε-bounded codes. Israel J. Math. 29 (1978), 205–220. [48] Palmer, M. R., Parry, W. and Walters, P.. Large sets of endomorphisms and of g-measures. The Structure of Attractors in Dynamical Systems (Proc. Conf., North Dakota State University, Fargo, ND, 1977) (Lecture Notes in Mathematics, 668). Eds. N. G. Markley, J. C. Martin and W. Perrizo. Springer, Berlin, 1978, pp. 191–210. [49] Helson, H. and Parry, W.. Cocycles and spectra. Ark. Mat. 16(2) (1978), 195–206. [50] Parry, W.. An information obstruction to finite expected coding length. Ergodic Theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1978) (Lecture Notes in Mathematics, 729). Springer, Berlin, 1979, pp. 163–168. [51] Parry, W.. Finitary isomorphisms with finite expected code lengths. Bull. London Math. Soc. 11 (1979), 170–176. [52] Parry, W.. The Lorenz attractor and a related population model. Ergodic Theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1978) (Lecture Notes in Mathematics, 729). Eds. M. Denker and K. Jacobs. Springer, Berlin, 1979, pp. 169–187. [53] Parry, W.. Topics in Ergodic Theory (Cambridge Tracts in Mathematics, 75). Cambridge University Press, Cambridge, 1981. [54] Parry, W.. Finitary isomorphisms with finite expected code-lengths. II. J. London Math. Soc. (2) 24 (1981), 569–576. [55] Parry, W.. Self-generation of self-replicating maps of an interval. Ergod. Th. & Dynam. Sys. 1 (1981), 197–208. [56] Parry, W. and Tuncel, S.. On the classification of Markov chains by finite equivalence. Ergod. Th. & Dynam. Sys. 1 (1981), 303–335. [57] Parry, W.. The classification of topological Markov chains: adapted shift equivalence. Israel J. Math. 38 (1981), 335–344. [58] Parry, W. and Tuncel, S.. Classification Problems in Ergodic Theory (London Mathematical Society Lecture Note Series, 67). Cambridge University Press, Cambridge, 1982. [59] Parry, W. and Tuncel, S.. On the stochastic and topological structure of Markov chains. Bull. London Math. Soc. 14 (1982), 16–27. [60] Parry, W. and Tuncel, S.. Two classification problems for finite state Markov chains. Ergodic Theory and Related Topics (Proc. Conf., Vitte, 1981) (Mathematical Research, 12). Ed. H. Michel. Akademie-Verlag, Berlin, 1982, pp. 153–159. [61] Parry, W.. An analogue of the prime number theorem for closed orbits of shifts of finite type and their suspensions. Israel J. Math. 45 (1983), 41–52. [62] Parry, W. and Pollicott, M.. An analogue of the prime number theorem for closed orbits of Axiom A flows. Ann. of Math. (2) 118 (1983), 573–591. [63] Parry, W. and Schmidt, K.. Invariants of finitary isomorphisms with finite expected code-lengths. Conference in Modern Analysis and Probability (New Haven, CT, 1982) (Contemporary Mathematics, 26). Eds. R. Beals, A. Beck, A. Bellow and A. Hajian. American Mathematical Society, Providence, RI, 1984, pp. 301–307. [64] Parry, W. and Schmidt, K.. Natural coefficients and invariants for Markov-shifts. Invent. Math. 76 (1984), 15–32. [65] Parry, W.. Bowen’s equidistribution theory and the Dirichlet density theorem. Ergod. Th. & Dynam. Sys. 4 (1984), 117–134. [67] Parry, W. and Pollicott, M.. The Chebotarov theorem for Galois coverings of Axiom A flows. Ergod. Th. & Dynam. Sys. 6 (1986), 133–148. [68] Parry, W.. Synchronisation of canonical measures for hyperbolic attractors. Comm. Math. Phys. 106 (1986), 267–275. [69] Alexander, J. C. and Parry, W.. Discerning fat baker’s transformations. Dynamical Systems (College Park, MD, 1986–87) (Lecture Notes in Mathematics, 1342). Springer, Berlin, 1988, pp. 1–6. [70] Parry, W.. Equilibrium states and weighted uniform distribution of closed orbits. Dynamical Systems (College Park, MD, 1986–87) (Lecture Notes in Mathematics, 1342). Springer, Berlin, 1988,pp. 617–625. [71] Parry, W.. Problems and perspectives in the theory of Markov shifts. Dynamical Systems (College Park, MD, 1986–87) (Lecture Notes in Mathematics, 1342). Springer, Berlin, 1988, pp. 626–637. [72] Parry, W.. Decoding with two independent processes. Measure and Measurable Dynamics (Rochester, NY, 1987) (Contemporary Mathematics, 94). Eds. R. D. Mauldin, R. M. Shortt and C. E. Silva. American Mathematical Society, Providence, RI, 1989, pp. 207–209. [73] Parry, W.. Temporal and spatial distribution of closed orbits of hyperbolic dynamical systems. Measure and Measurable Dynamics (Rochester, NY, 1987) (Contemporary Mathematics, 94). Eds. R. D. Mauldin, R. M. Shortt and C. E. Silva. American Mathematical Society, Providence, RI, 1989, pp. 211–216. [74] Coelho, Z. and Parry, W.. Central limit asymptotics for shifts of finite type. Israel J. Math. 69 (1990), 235–249. [75] Parry, W. and Pollicott, M.. Zeta functions and the periodic orbit structure of hyperbolic dynamics. Astérisque 187–188 (1990), 1–268. [76] Parry, W.. Notes on coding problems for finite state processes. Bull. London Math. Soc. 23 (1991), 1–33. [77] Parry, W.. A cocycle equation for shifts. Symbolic Dynamics and its Applications (New Haven, CT, 1991) (Contemporary Mathematics, 135). Ed. P. Walters. American Mathematical Society, Providence, RI, 1992, pp. 327–333. [78] Parry, W.. In general a degree two map is an automorphism. Symbolic Dynamics and its Applications (New Haven, CT, 1991) (Contemporary Mathematics, 135). Ed. P. Walters. American Mathematical Society, Providence, RI, 1992, pp. 335–338. [79] Noorani, M. S. M. and Parry, W.. A Chebotarev theorem for finite homogeneous extensions of shifts. Bol. Soc. Brasil. Mat. (N.S.) 23 (1992), 137–151. [80] Parry, W.. Remarks on Williams’ problem. Differential Equations, Dynamical Systems, and Control Science (Lecture Notes in Pure and Applied Mathematics, 152). Eds. K. D. Elworthy, W. N. Everitt and E. B. Lee. Dekker, New York, 1994, pp. 235–246. [82] Parry, W.. Instances of cohomological triviality and rigidity. Ergod. Th. & Dynam. Sys. 15 (1995), 685–696. [83] Parry, W.. Ergodic properties of a one-parameter family of skew-products. Nonlinearity 8 (1995), 821–825. [84] Parry, W.. Automorphisms of the Bernoulli endomorphism and a class of skew-products. Ergod. Th. & Dynam. Sys. 16 (1996), 519–529. [85] W. Parry. Squaring and cubing the circle–Rudolph’s theorem. Ergodic Theory of $\protect \mathbb {Z}^d$ Actions (Warwick, 1993–1994) (London Mathematical Society Lecture Note Series, 228). Eds. M. Pollicott and K. Schmidt. Cambridge University Press, Cambridge, 1996, pp. 177–183. [86] Parry, W.. Cohomology of permutative cellular automata. Israel J. Math. 99 (1997), 315–333. [87] Parry, W.. Skew products of shifts with a compact Lie group. J. London Math. Soc. (2) 56 (1997), 395–404. [88] Parry, W. and Pollicott, M.. The Livšic cocycle equation for compact Lie group extensions of hyperbolic systems. J. London Math. Soc. (2) 56 (1997), 405–416. [89] Parry, W. and Pollicott, M.. Stability of mixing for toral extensions of hyperbolic systems. Proc. Steklov Inst. Math. 216 (1997), 350–359. [90] Coelho, Z., Parry, W. and Williams, R.. A note on Livšic’s periodic point theorem. Topological Dynamics and Applications (Contemporary Mathematics, 215). American Mathematical Society, Providence, RI, 1998, pp. 223–230. [91] Coelho, Z. and Parry, W.. Shift endomorphisms and compact Lie extensions. Bol. Soc. Brasil. Mat. (N.S.) 29 (1998), 163–179. [93] Field, M. and Parry, W.. Stable ergodicity of skew extensions by compact Lie groups. Topology 38 (1999), 167–187. [94] Parry, W.. The Livšic periodic point theorem for non-abelian cocycles. Ergod. Th. & Dynam. Sys. 19 (1999), 687–701. [95] Coelho, Z. and Parry, W.. Ergodicity of p-adic multiplications and the distribution of Fibonacci numbers. Topology, Ergodic Theory, Real Algebraic Geometry (American Mathematical Society Translation Series 2, 202). Eds. V. Turaev and A. Vershik. American Mathematical Society, Providence, RI, 2001, pp. 51–70. [96] Parry, W. and Pollicott, M.. Skew products and Livˇsic theory. Representation Theory, Dynamical Systems, and Asymptotic Combinatorics (American Mathematical Society Translation Series 2, 217). Eds. V. Kaimanovich and A. Lodkin. American Mathematical Society, Providence, RI, 2006, pp. 139–165. [97] Parry, W. and Pollicott, M.. An analogue of Bauer’s theorem for closed orbits of skew products. Ergod. Th. & Dynam. Sys. 28 (2008), 535–546. [98] Hamdan, D., Parry, W. and Thouvenot, J.-P.. Shannon entropy for stationary processes and dynamical systems. Ergod. Th. & Dynam. Sys. 28 (2008), 447–480. [99] Parry, W.. An elementary construction of Cr renormalizing maps, volume in honour of Zeeman’s 60th Birthday, unpublished. Other articles cited in the survey [100] Ashley, J.. Bounded-to-1 factors of an aperiodic shift of finite type are 1-to-1 almost everywhere factors also. Ergod. Th. & Dynam. Sys. 10 (1990), 615–625. [101] Bowen, R.. The equidistribution of closed geodesics. Amer. J. Math. 94 (1972), 413–423. [102] Bowen, R.. Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms (Lecture Notes in Mathematics, 470). Springer, Berlin, 1975. [103] Bowen, R. and Franks, J.. Homology for zero-dimensional nonwandering sets. Ann. of Math. (2) 106 (1977), 73–92. [104] Franks, J.. Flow equivalence of subshifts of finite type. Ergod. Th. & Dynam. Sys. 4 (1984), 53–66. [105] Friedman, N. A. and Ornstein, D. S.. On isomorphism of weak Bernoulli transformations. Adv. Math. 5 (1970), 365–394. [106] Kim, K. H. and Roush, F. W.. The Williams conjecture is false for irreducible subshifts. Ann. of Math. (2) 149 (1999), 545–558. [107] Marcus, B. and Tuncel, S.. Matrices of polynomials, positivity, and finite equivalence of Markov chains. J. Amer. Math. Soc. 6 (1993), 131–147. [108] Margulis, G. A.. On Some Aspects of the Theory of Anosov Systems (With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows). Springer, Berlin, 2004. [109] Morris, D. W.. Ratner’s Theorems on Unipotent Flows (Chicago Lectures in Mathematics). University of Chicago Press, Chicago, IL, 2005. [110] Nogueira, A.. The three-dimensional Poincaré continued fraction algorithm. Israel J. Math. 90(1–3) (1995), 373–401. [111] Ornstein, D.. Bernoulli shifts with the same entropy are isomorphic. Adv. Math. 4 (1970), 337–352. [112] Rohlin, V. A.. Lectures on the entropy theory of transformations with invariant measure. Uspehi Mat. Nauk 22 (1967), 3–56 (in Russian). [113] Ruelle, D.. A variational formulation of equilibrium statistical mechanics and the Gibbs phase rule. Comm. Math. Phys. 5 (1967), 324–329. [114] Schmidt, K.. Invariants for finitary isom |