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

Gianpiero Cattaneo; Alberto Dennunzio; Fabio Farina

RAIRO - Theoretical Informatics and Applications (2006)

- Volume: 40, Issue: 2, page 333-352
- ISSN: 0988-3754

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topCattaneo, Gianpiero, Dennunzio, Alberto, and Farina, Fabio. "A survey on transitivity in discrete time dynamical systems. application to symbolic systems and related languages." RAIRO - Theoretical Informatics and Applications 40.2 (2006): 333-352. <http://eudml.org/doc/249686>.

@article{Cattaneo2006,

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.
},

author = {Cattaneo, Gianpiero, Dennunzio, Alberto, Farina, Fabio},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Transitivity; chaos; symbolic dynamics;
formal languages.; formal languages; topological mixing},

language = {eng},

month = {7},

number = {2},

pages = {333-352},

publisher = {EDP Sciences},

title = {A survey on transitivity in discrete time dynamical systems. application to symbolic systems and related languages},

url = {http://eudml.org/doc/249686},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Cattaneo, Gianpiero

AU - Dennunzio, Alberto

AU - Farina, Fabio

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

JO - RAIRO - Theoretical Informatics and Applications

DA - 2006/7//

PB - EDP Sciences

VL - 40

IS - 2

SP - 333

EP - 352

AB -
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.

LA - eng

KW - Transitivity; chaos; symbolic dynamics;
formal languages.; formal languages; topological mixing

UR - http://eudml.org/doc/249686

ER -

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