The Topological Pressure of Linear Cellular Automata
by
Jung-Chao Ban 1, 2 and Chih-Hung Chang 3,*
Jung-Chao Ban 1, 2 and Chih-Hung Chang 3,*
1
Department of Applied Mathematics, National Dong Hwa University, 97063, Hualian, Taiwan, R.O.C.
2
Taida Institute for Mathematical Sciences, National Taiwan University, 10617, Taipei, Taiwan, R.O.C.
3
National Center for Theoretical Sciences, Mathematics Division, National Tsing Hua University, 30043, Hsinchu, Taiwan, R.O.C.
*
Author to whom correspondence should be addressed.
Entropy 2009, 11(2), 271-284; https://doi.org/10.3390/e11020271
Received: 13 April 2009 / Accepted: 6 May 2009 / Published: 11 May 2009
This elucidation studies ergodicity and equilibrium measures for additive cellular automata with prime states. Additive cellular automata are ergodic with respect to Bernoulli measure unless it is either an identity map or constant. The formulae of measure-theoretic and topological entropies can be expressed in closed forms and the topological pressure is demonstrated explicitly for potential functions that depend on finitely many coordinates. According to these results, Parry measure is inferred to be an equilibrium measure.
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Keywords:
Cellular automata; additive; equilibrium measure
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MDPI and ACS Style
Ban, J.-C.; Chang, C.-H. The Topological Pressure of Linear Cellular Automata. Entropy 2009, 11, 271-284.
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