# Concept derivation guides

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Concept guide



## [Discrete-time dynamical system: iterating T(x)=(3x+1) mod 7 on seven states](/en/derivations/derivation-mko-discrete-dynamical-system-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-discrete-dynamical-system)

State space X={0,1,2,3,4,5,6}, update map T(x)=(3x+1) mod 7. From x_0=0 compute the orbit given by x_(n+1)=T(x_n), prove x_(n+6)=x_n for every natural number n and use it to find x_2026; enumerate the fixed points completely; decide that A={0,1,2,4,5,6} is forward invariant while B={0,1} is not, and prove that the orbit from 0 never reaches the fixed point.

Discrete-time dynamical system

derivation-mko-discrete-dynamical-system-01





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