Displaying similar documents to “The second machine class 2, an encyclopedic view on the parallel computation thesis”

Non-transitive points and porosity

T. K. Subrahmonian Moothathu (2013)

Colloquium Mathematicae

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We establish that for a fairly general class of topologically transitive dynamical systems, the set of non-transitive points is very small when the rate of transitivity is very high. The notion of smallness that we consider here is that of σ-porosity, and in particular we show that the set of non-transitive points is σ-porous for any subshift that is a factor of a transitive subshift of finite type, and for the tent map of [0,1]. The result extends to some finite-to-one factor systems....

A survey on transitivity in discrete time dynamical systems. application to symbolic systems and related languages

Gianpiero Cattaneo, Alberto Dennunzio, Fabio Farina (2006)

RAIRO - Theoretical Informatics and Applications

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The main goal of this paper is the investigation of a relevant property which appears in the various definition of deterministic topological chaos for discrete time dynamical system: transitivity. Starting from the standard Devaney's notion of topological chaos based on regularity, transitivity, and sensitivity to the initial conditions, the critique formulated by Knudsen is taken into account in order to exclude periodic chaos from this definition. Transitivity (or some stronger versions...