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 of it) turns out to be the relevant condition of chaos and its role is discussed by a survey of some important results about it with the presentation of some new results. In particular, we study topological mixing, strong transitivity, and full transitivity. Their applications to symbolic dynamics are investigated with respect to the relationships with the associated languages. © EDP Sciences 2006.

Cattaneo, G., Dennunzio, A., Farina, F. (2006). A survey on transitivity in discrete time dynamical systems. Applications to symbolic systems and related languages. RAIRO. INFORMATIQUE THEORIQUE ET APPLICATIONS, 40, 333-352 [10.1051/ita:2006016].

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

CATTANEO, GIANPIERO;DENNUNZIO, ALBERTO;FARINA, FABIO MARIO
2006

Abstract

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 of it) turns out to be the relevant condition of chaos and its role is discussed by a survey of some important results about it with the presentation of some new results. In particular, we study topological mixing, strong transitivity, and full transitivity. Their applications to symbolic dynamics are investigated with respect to the relationships with the associated languages. © EDP Sciences 2006.
Articolo in rivista - Articolo scientifico
chaos, formal languages, symbolic dynamics, transitivity
English
333
352
Cattaneo, G., Dennunzio, A., Farina, F. (2006). A survey on transitivity in discrete time dynamical systems. Applications to symbolic systems and related languages. RAIRO. INFORMATIQUE THEORIQUE ET APPLICATIONS, 40, 333-352 [10.1051/ita:2006016].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/15002
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