# Substitution systems associated with the dynamical system (𝒜, Tf)*

Maria de Fátima Correia; Carlos Ramos; Sandra Vinagre

ESAIM: Proceedings (2012)

- Volume: 36, page 159-169
- ISSN: 1270-900X

## Access Full Article

top## Abstract

top## How to cite

topCorreia, Maria de Fátima, Ramos, Carlos, and Vinagre, Sandra. Fournier-Prunaret, D., Gardini, L., and Reich, L., eds. " Substitution systems associated with the dynamical system (𝒜, Tf)*." ESAIM: Proceedings 36 (2012): 159-169. <http://eudml.org/doc/251266>.

@article{Correia2012,

abstract = {We consider the dynamical system
(𝒜, Tf), where
𝒜 is a class of differential real functions defined on some interval and
Tf : 𝒜 → 𝒜 is an operator Tfφ := fοφ, where f is a differentiable m-modal map. If we consider functions in
𝒜 whose critical values are periodic points for f then, we show how to define and characterize a substitution system associated with
(𝒜, Tf). For these substitution systems, we compute the growth rate of the new critical points, and observe that this growth is independent of the initial conditions.},

author = {Correia, Maria de Fátima, Ramos, Carlos, Vinagre, Sandra},

editor = {Fournier-Prunaret, D., Gardini, L., Reich, L.},

journal = {ESAIM: Proceedings},

keywords = {Infinite dimensional dynamical systems; Iteration theory; Symbolic dynamics; Substitution systems; infinite dimensional dynamical systems; iteration theory; symbolic dynamics; substitution systems},

language = {eng},

month = {8},

pages = {159-169},

publisher = {EDP Sciences},

title = { Substitution systems associated with the dynamical system (𝒜, Tf)*},

url = {http://eudml.org/doc/251266},

volume = {36},

year = {2012},

}

TY - JOUR

AU - Correia, Maria de Fátima

AU - Ramos, Carlos

AU - Vinagre, Sandra

AU - Fournier-Prunaret, D.

AU - Gardini, L.

AU - Reich, L.

TI - Substitution systems associated with the dynamical system (𝒜, Tf)*

JO - ESAIM: Proceedings

DA - 2012/8//

PB - EDP Sciences

VL - 36

SP - 159

EP - 169

AB - We consider the dynamical system
(𝒜, Tf), where
𝒜 is a class of differential real functions defined on some interval and
Tf : 𝒜 → 𝒜 is an operator Tfφ := fοφ, where f is a differentiable m-modal map. If we consider functions in
𝒜 whose critical values are periodic points for f then, we show how to define and characterize a substitution system associated with
(𝒜, Tf). For these substitution systems, we compute the growth rate of the new critical points, and observe that this growth is independent of the initial conditions.

LA - eng

KW - Infinite dimensional dynamical systems; Iteration theory; Symbolic dynamics; Substitution systems; infinite dimensional dynamical systems; iteration theory; symbolic dynamics; substitution systems

UR - http://eudml.org/doc/251266

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.