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Ergodic Theory: with a view towards Number Theory
Motivation.- Ergodicity, Recurrence and Mixing.- Continued Fractions.- Invariant Measures for Continuous Maps.- Conditional Measures and Algebras.- Factors and Joinings.- Furstenberg's Proof ofExpand
Mahler measure and entropy for commuting automorphisms of compact groups
SummaryWe compute the joint entropy ofd commuting automorphisms of a compact metrizable group. LetRd = ℤ[u1±1,...,[d1±1] be the ring of Laurent polynomials ind commuting variables, andM beExpand
Additive Cellular Automata and Volume Growth
  • T. Ward
  • Mathematics, Computer Science
  • Entropy
  • 2000
A class of dynamical systems associated to rings of S-integers in rational function fields is described. Expand
Heights of Polynomials and Entropy in Algebraic Dynamics
The main theme of the book is the theory of heights as they appear in various guises. This includes a large body of results on Mahler's measure of the height of a polynomial of which topic there isExpand
S-integer dynamical systems: periodic points.
We associate via duality a dynamical system to each pair (RS,x), where RS is the ring of S-integers in an A-field k, and x is an element of RS\{0}. These dynamical systems include the circle doublingExpand
Recurrence Sequences
We survey a selection of number-theoretic properties of linear recurrence sequences together with their direct generalizations. Expand
Arithmetic and growth of periodic orbits
Two natural properties of integer sequences are introduced and studied. The first, exact realizability, is the property that the sequence coincides with the number of periodic points under some map.Expand
Automorphisms of solenoids and p -adic entropy
We show that a full solenoid is locally the product of a euclidean component and p-adic components for each rational prime p. An automorphism of a solenoid preserves these components, and itsExpand
The Abramov-Rokhlin entropy addition formula for amenable group actions
In this note we show that the entropy of a skew product action of a countable amenable group satisfies the classical formula of Abramov and Rokhlin.
A polynomial Zsigmondy theorem
We find an analogue of the primitive divisor results of Bang and Zsigmondy in polynomial rings.