Basic concepts of classical dynamics are analysed in the simple mathematical setting of state transition systems, where both time and space are discrete, and no structure is assumed on the state space besides a binary transition relation. This framework proves useful to the dynamical analysis of computations and biomolecular processes. A relational formulation of this framework is presented in this paper, where the concepts of attractor and recurrence surface in two variants, respectively relating to the two fundamental modalities. A strong link between recurrence and both existence and extent of attractors, in either variant, is established by a novel characterization theorem.
Relational state transition dynamics
FRANCO, Giuditta;MANCA, Vincenzo
2008-01-01
Abstract
Basic concepts of classical dynamics are analysed in the simple mathematical setting of state transition systems, where both time and space are discrete, and no structure is assumed on the state space besides a binary transition relation. This framework proves useful to the dynamical analysis of computations and biomolecular processes. A relational formulation of this framework is presented in this paper, where the concepts of attractor and recurrence surface in two variants, respectively relating to the two fundamental modalities. A strong link between recurrence and both existence and extent of attractors, in either variant, is established by a novel characterization theorem.
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