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A comment on the definition of relative pressure
Karl Petersen, Sujin Shin
We show that two natural definitions of the relative pressure function for a locally constant potential function and a factor map from a shift of finite type coincide almost everyw…
Dynamical properties of the Pascal adic transformation
Xavier Mela, Karl Petersen
We study the dynamics of a transformation that acts on infinite paths in the graph associated with Pascal's triangle. For each ergodic invariant measure the asymptotic law of the r…
Measures of maximal relative entropy
Karl Petersen, Anthony Quas, Sujin Shin
Given an irreducible subshift of finite type X, a subshift Y, a factor map π: X \to Y, and an ergodic invariant measure νon Y, there can exist more than one ergodic measure on X wh…
Easy and nearly simultaneous proofs of the Ergodic Theorem and Maximal Ergodic Theorem
Karl Petersen
A very short and direct proof along the lines of the Kamae-Katznelson-Weiss approach.
Factor maps between tiling dynamical systems
Karl Petersen
We show that there is no Curtis-Hedlund-Lyndon Theorem for factor maps between tiling dynamical systems: there are codes between such systems which cannot be achieved by working wi…
Binomial-coefficient multiples of irrationals
Terrence M. Adams, Karl E. Petersen
Denote by a random infinite path in the graph of Pascal's triangle (left and right turns are selected independently with fixed probabilities) and by the binomial coeff…