# Dynamical system map in Lean Six Sigma

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There are quite a few books where we can find terms used in Lean Six Sigma methodology. The topic is not whether we use the same technical terms since Lean Six Sigma uses knowledge of statistics, mathematics, project management, psychology, and business operations, but rather on developing new maps for Lean Six Sigma.
The map that I will refer is the map of the theory of dynamical systems, which is a map that denotes an evolutionary function used to create discrete dynamical systems. Any dynamic system has a chaotic behavior and is a generator of fractals. In evolution systems we have an evolution in time of a system.

To be able to design and construct dynamical systems in Lean Six Sigma we will need to ensure that there is a certain chaos and that many fractals are developed. An example of fractals are projects that would have the same pattern and present an isomorphic behavior. The systems that are closed and where we do not understand their evolution will not be able to use the limit set that is the state a dynamical system that is reached after an infinite amount of time has passed, by either going forward or backwards in time. Limit sets are important because they can be used to understand the long term behavior of a dynamical system. Once we eliminate the smoothing of space-time, we can develop and design the dynamic systems as part of Lean Six Sigma environment. Now, if we refer to single-particle states the concentration is missing. If we want to characterize the dynamics of a single particle, we need to look at its possible trajectories which is a sequence of events that the particle can take as it hops back and forth between its two states. If we break each trajectory into two-step piece, we are in fact using a Markov model. In a Markov model, the probability of jumping to a particular state at a time "t" depends only on that particular state and what state it jumps from, and does not depend on the probabilities of the earliest states in the trajectory. If we connect the dynamic system map to a Lean Six Sigma environment we will see many trajectories that will be moving back and forth as one of the system's characteristics. Since time and space can only be measured over large intervals, the concept of developing fast projects is in fact false under both Markov's model and dynamical system model map.