Additive conserved quantities in discrete-time lattice dynamical systems

Tetsuya Hattori, Shinji Takesue

Research output: Contribution to journalArticlepeer-review

63 Citations (Scopus)


We give a necessary and sufficient condition for the existence of additive conserved quantities for one-dimensional discrete-time lattice dynamical systems such as cellular automata (CA) and coupled map lattices. Proof is given for the case of nearest-neighbor interaction rules. The obtained condition guarantees the existence of the current conservation law and is useful for finding additive conserved quantities for CA. Applications are made to Wolfram's elementary CA and elementary reversible CA of Takesue. In the latter case, the additive conserved quantities are classified into those induced by local conservation laws and propagative ones.

Original languageEnglish
Pages (from-to)295-322
Number of pages28
JournalPhysica D: Nonlinear Phenomena
Issue number3
Publication statusPublished - 1991 Apr 2
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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