Dynamical Properties of Additive Cellular Automata over Finite Abelian Groups

O157; Some dynamical properties were discussed for additive cellular automata(CA)over finite abelian groups.These properties include surjection,ergodicity,sensitivity to initial conditions and positive expansivity.Some necessary and sufficient conditions of determining ergodicity and sensitivity of...

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Published in东华大学学报（英文版） Vol. 40; no. 1; pp. 116 - 121
Main Authors DENG Aiping, WANG Fengjie, WU Chenchen
Format Journal Article
LanguageEnglish
Published College of Science,Donghua University,Shanghai 201620,China 2023
Subjects
finite abelian group
additive cellular automaton
sensitivity to initial condition
ergodicity
positive expansivity
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Summary:O157; Some dynamical properties were discussed for additive cellular automata(CA)over finite abelian groups.These properties include surjection,ergodicity,sensitivity to initial conditions and positive expansivity.Some necessary and sufficient conditions of determining ergodicity and sensitivity of the above additive CA were presented,respectively.A necessary condition for the positive expansivity of the above additive CA was given.The positive expansivity was proved to be preserved under the shift mappings for the general CA.The discussion was mainly based on the structure theorem of the finite abelian groups and the matrix associated with the global rule of the additive CA over the finite abelian p-groups.
ISSN:1672-5220
DOI:10.19884/j.1672-5220.202112003