Dynamical systems on monoids have been recently proposed as minimal mathematical models for the intuitive notion of deterministic dynamics. This paper shows that any dynamical system DS_L on a monoid L can be exhaustively decomposed into a family of mutually disconnected subsystems—the constituent systems of DS_L . In addition, constituent systems are themselves indecomposable, even though they may very well be complex. Finally, this work also makes clear how any dynamical system DS_L turns out to be identical to the sum of all its constituent systems. Constituent systems can thus be thought as the indecomposable, but possibly complex, building blocks to which the dynamics of an arbitrary complex system fully reduces. However, no further reduction of the constituents is possible, even if they are themselves complex.

Decomposing Dynamical Systems

GIUNTI, MARCO
2016

Abstract

Dynamical systems on monoids have been recently proposed as minimal mathematical models for the intuitive notion of deterministic dynamics. This paper shows that any dynamical system DS_L on a monoid L can be exhaustively decomposed into a family of mutually disconnected subsystems—the constituent systems of DS_L . In addition, constituent systems are themselves indecomposable, even though they may very well be complex. Finally, this work also makes clear how any dynamical system DS_L turns out to be identical to the sum of all its constituent systems. Constituent systems can thus be thought as the indecomposable, but possibly complex, building blocks to which the dynamics of an arbitrary complex system fully reduces. However, no further reduction of the constituents is possible, even if they are themselves complex.
9783319243917
Deterministic dynamical system; complex system; reduction; constituent system; dynamical system on a monoid; dynamical system over a semigroup
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/139313
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