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On the genesis of symbolic dynamics as we know it

100%

Coven E., Nitecki Z.

Colloquium Mathematicum

2008

tom 110

nr 2

227-242

We trace the beginning of symbolic dynamics-the study of the shift dynamical system-as it arose from the use of coding to study recurrence and transitivity of geodesics. It is our assertion that neither Hadamard's 1898 paper, nor the Morse-Hedlund papers of 1938 and 1940, which are normally cited as the first instances of symbolic dynamics, truly present the abstract point of view associated with the subject today. Based in part on the evidence of a 1941 letter from Hedlund to Morse, we place the beginning of symbolic dynamics in a paper published by Hedlund in 1944.

Embedding odometers in cellular automata

100%

Coven E., Yassawi R.

Fundamenta Mathematicae

2009

tom 206

nr 1

131-138

We consider the problem of embedding odometers in one-dimensional cellular automata. We show that (1) every odometer can be embedded in a gliders-with-reflecting-walls cellular automaton, which one depending on the odometer, and (2) an odometer can be embedded in a cellular automaton with local rule $x_i ↦ x_i + x_{i+1} mod n$ (i ∈ ℤ), where n depends on the odometer, if and only if it is "finitary."

Ograniczanie wyników

1 Colloquium Mathematicum

1 Fundamenta Mathematicae

2 Coven E.

1 Nitecki Z.

1 Yassawi R.

1 2009

1 2008

Wyniki wyszukiwania

On the genesis of symbolic dynamics as we know it

Embedding odometers in cellular automata