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The mathematical research of William Parry FRS \ud

By Mark Pollicott, Richard Sharp, S. Tuncel and Peter Walters

Abstract

In this article we survey the mathematical research of the late William (Bill) Parry, FRS.\ud \u

Topics: QA
Publisher: Cambridge University Press
Year: 2008
OAI identifier: oai:wrap.warwick.ac.uk:682

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Citations

  1. Papers authored by William Parry
  2. (1960). On the β-expansions of real numbers. doi
  3. (1962). Ergodic properties of some permutation processes. doi
  4. (1963). Infinite measure preserving transformations with mixing. doi
  5. (1963). An ergodic theorem of information theory without invariant measure. doi
  6. (1964). Intrinsic Markov chains. doi
  7. (1964). On Rohlin’s formula for entropy. doi
  8. (1964). Note on the ergodic theorem of Hurewicz. doi
  9. (1964). Representations for real numbers. doi
  10. (1965). Minimal dynamical systems with quasi-discrete spectrum. doi
  11. (1965). Ergodic and spectral analysis of certain infinite measure preserving transformations. doi
  12. (1966). Affine transformations with quasi-discrete spectrum. doi
  13. (1966). Symbolic dynamics and transformations of the unit interval. doi
  14. (1966). On the coincidence of three invariant σ-algebras associated with an affine transformation. doi
  15. (1966). Semi-groups of affine transformations. doi
  16. (1966). On a factor automorphism of a normal dynamical system. doi
  17. (1967). On the periodic points of certain automorphisms and a system of polynomial identities. doi
  18. (1967). Principal partitions and generators. doi
  19. (1967). Generators for perfect partitions. doi
  20. (1968). Aperiodic transformations and generators. doi
  21. (1968). Some characteristic properties of dynamical systems with quasi-discrete spectra. doi
  22. (1967). Zero entropy of distal and related transformations. Topological Dynamics (Symposium,
  23. (1969). Ergodic properties of affine transformations and flows on nilmanifolds. doi
  24. (1969). Compact abelian group extensions of discrete dynamical systems. doi
  25. (1969). Entropy and Generators in Ergodic Theory. doi
  26. (1970). Spectral analysis of G-extensions of dynamical systems. doi
  27. (1970). Dynamical systems on nilmanifolds. doi
  28. (1970). Minimal skew-product homeomorphisms and coalescence.
  29. (1971). Metric classification of ergodic nilflows and unipotent affines. doi
  30. (1971). Ergodic theory of G-spaces. Actes du Congr`
  31. (1974). Endomorphisms of a Lebesgue space. doi
  32. (1972). Stability of group representations and Haar spectrum. doi
  33. (1972). Cocycles and velocity changes. doi
  34. (1972). Compact abelian group extensions of dynamical systems. doi
  35. (1973). Dynamical representations in nilmanifolds.
  36. (1973). Notes on a posthumous paper by doi
  37. (1972). Class properties of dynamical systems. Recent Advances in Topological Dynamics (Proc. Conf., Yale University, doi
  38. (1974). A note on cocycles in ergodic theory.
  39. (1975). A topological invariant of flows on 1-dimensional spaces. doi
  40. (1976). A note on cocycles of unitary representations. doi
  41. (1976). Some classification problems in ergodic theory. doi
  42. (1977). Block coding and a zeta function for finite Markov chains. doi
  43. (1977). A finitary classification of topological Markov chains and sofic systems. doi
  44. (1978). The information cocycle and ε-bounded codes. doi
  45. (1977). Large sets of endomorphisms and of g-measures. doi
  46. (1978). Cocycles and spectra. doi
  47. (1978). An information obstruction to finite expected coding length. Ergodic Theory (Proc. doi
  48. (1979). Finitary isomorphisms with finite expected code lengths. doi
  49. (1978). The Lorenz attractor and a related population model. Ergodic Theory (Proc. doi
  50. (1981). Topics in Ergodic Theory (Cambridge Tracts in doi
  51. (1981). Finitary isomorphisms with finite expected code-lengths. doi
  52. (1981). Self-generation of self-replicating maps of an interval. doi
  53. (1981). On the classification of Markov chains by finite equivalence. doi
  54. (1981). The classification of topological Markov chains: adapted shift equivalence. doi
  55. (1982). Classification Problems in Ergodic Theory (London doi
  56. (1982). On the stochastic and topological structure of Markov chains. doi
  57. (1981). Two classification problems for finite state Markov chains. Ergodic Theory and Related Topics (Proc. Conf., Vitte,
  58. (1983). An analogue of the prime number theorem for closed orbits of shifts of finite type and their suspensions. doi
  59. (1983). An analogue of the prime number theorem for closed orbits of Axiom A flows. doi
  60. (1982). Invariants of finitary isomorphisms with finite expected code-lengths. doi
  61. (1984). Natural coefficients and invariants for Markov-shifts. doi
  62. (1984). Bowen’s equidistribution theory and the Dirichlet density theorem. doi
  63. (1986). The Chebotarov theorem for Galois coverings of Axiom A flows. doi
  64. (1986). Synchronisation of canonical measures for hyperbolic attractors. doi
  65. (1988). Discerning fat baker’s transformations. Dynamical Systems (College Park, doi
  66. (1988). Equilibrium states and weighted uniform distribution of closed orbits. doi
  67. (1988). Problems and perspectives in the theory of Markov shifts. doi
  68. (1987). Decoding with two independent processes. Measure and Measurable Dynamics doi
  69. (1987). Temporal and spatial distribution of closed orbits of hyperbolic dynamical systems. Measure and Measurable Dynamics doi
  70. (1990). Central limit asymptotics for shifts of finite type. doi
  71. (1990). Zeta functions and the periodic orbit structure of hyperbolic dynamics.
  72. (1991). Notes on coding problems for finite state processes. doi
  73. (1991). A cocycle equation for shifts. Symbolic Dynamics and its Applications doi
  74. (1991). In general a degree two map is an automorphism. Symbolic Dynamics and its Applications doi
  75. (1992). A Chebotarev theorem for finite homogeneous extensions of shifts. doi
  76. (1994). Remarks on Williams’ problem. Differential Equations, Dynamical Systems,
  77. (1995). Instances of cohomological triviality and rigidity. doi
  78. (1995). Ergodic properties of a one-parameter family of skew-products. doi
  79. (1996). Automorphisms of the Bernoulli endomorphism and a class of skew-products. doi
  80. (1993). Squaring and cubing the circle–Rudolph’s theorem. Ergodic Theory of Zd Actions doi
  81. (1997). Cohomology of permutative cellular automata. doi
  82. (1997). Skew products of shifts with a compact Lie group. doi
  83. (1997). The Livˇ sic cocycle equation for compact Lie group extensions of hyperbolic systems. doi
  84. (1997). Stability of mixing for toral extensions of hyperbolic systems.
  85. (1998). A note on Livˇ sic’s periodic point theorem. doi
  86. (1998). Shift endomorphisms and compact Lie extensions. doi
  87. (1999). Stable ergodicity of skew extensions by compact Lie groups. doi
  88. (1999). The Livˇ sic periodic point theorem for non-abelian cocycles.
  89. (2001). Ergodicity of p-adic multiplications and the distribution of Fibonacci numbers. Topology, Ergodic Theory, Real Algebraic
  90. (2006). Skew products and Liˇ vsic theory. Representation Theory, Dynamical Systems,
  91. (2008). An analogue of Bauer’s theorem for closed orbits of skew products. doi
  92. (2008). Shannon entropy for stationary processes and dynamical systems. doi
  93. An elementary construction of Cr renormalizing maps, volume
  94. (1990). Bounded-to-1 factors of an aperiodic shift of finite type are 1-to-1 almost everywhere factors also. doi
  95. (1972). The equidistribution of closed geodesics. doi
  96. (1975). Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms doi
  97. (1977). Homology for zero-dimensional nonwandering sets. doi
  98. (1984). Flow equivalence of subshifts of finite type. doi
  99. (1970). On isomorphism of weak Bernoulli transformations. doi
  100. (1999). The Williams conjecture is false for irreducible subshifts. doi
  101. (1993). Matrices of polynomials, positivity, and finite equivalence of Markov chains. doi
  102. (2004). On Some Aspects of the Theory of Anosov Systems (With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows). doi
  103. (2005). Ratner’s Theorems on Unipotent Flows (Chicago Lectures in Mathematics).
  104. (1995). The three-dimensional Poincar´ e continued fraction algorithm. doi
  105. (1970). Bernoulli shifts with the same entropy are isomorphic. doi
  106. (1967). Lectures on the entropy theory of transformations with invariant measure.
  107. (1967). A variational formulation of equilibrium statistical mechanics and the Gibbs phase rule. doi
  108. (1984). Invariants for finitary isomorphisms with finite expected code lengths. doi
  109. (1999). Remarks on Livˇ sic’ theory for nonabelian cocycles.
  110. (1995). Ergodic Theory of Fibred Systems and Metric Number Theory
  111. (1985). Expanding endomorphisms of the circle revisited. doi
  112. (1967). Differentiable dynamical systems. doi
  113. (1975). A variational principle for the pressure of continuous transformations. doi
  114. (1973). Classification of subshifts of finite type. doi
  115. (1957). Representations for real numbers and their ergodic properties. doi
  116. (1965). Generators in ergodic theory II. Vestnik Leningrad.
  117. (2009). Similarity of Automorphisms of the Torus doi
  118. (1979). Topological Entropy and Equivalence of Dynamical Systems doi
  119. (1979). Bernoulli schemes of the same entropy are finitarily isomorphic. doi
  120. (1981). Conditional pressure and coding. doi
  121. (1983). On the finitary isomorphisms of Markov shifts that have finite expected coding time. doi
  122. (1976). Zeta-functions for expanding maps and Anosov flows. doi
  123. (1971). Livˇ sic. Certain properties of the homology of Y-systems.

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