Geodesic
Substitution systems associated with the dynamical system (𝒜, Tf)
Maria de Fátima Correia1 ; Carlos Ramos1 ; Sandra Vinagre1
1Department of Mathematics, University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
ESAIM. Proceedings, Tome 36 (2012), pp. 159-169
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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.
DOI : 10.1051/proc/201236012

Maria de Fátima Correia  1   ; Carlos Ramos  1   ; Sandra Vinagre  1

1 Department of Mathematics, University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal 
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     author = {Maria de F\'atima Correia and Carlos Ramos and Sandra Vinagre},
     title = {Substitution systems associated with the dynamical system {(\ensuremath{\mathscr{A}},} {Tf)}},
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Maria de Fátima Correia; Carlos Ramos; Sandra Vinagre. Substitution systems associated with the dynamical system (𝒜, Tf). ESAIM. Proceedings, Tome 36 (2012), pp. 159-169. doi: 10.1051/proc/201236012

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