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UID:8176@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150203T110000
DTEND;TZID=Europe/Paris:20150203T120000
DTSTAMP:20241120T210056Z
URL:https://www.i2m.univ-amu.fr/evenements/piecewise-contractions-defined-
 by-iterated-function-systems/
SUMMARY:Benito Pires (Universidade de São Paulo): Piecewise contractions d
 efined by iterated function systems
DESCRIPTION:Benito Pires: We are interested in the asymptotic behavior of p
 iecewise contractions of the interval (PCs). A map f : [0\, 1) → [0\, 1)
  is a PC of n intervals if there exists a partition of I = [0\, 1) into su
 bintervals I1\, . . . \, In such that each restriction f|Ii : Ii → I is 
 a Lipschitz-continuous contraction. We consider here an (n − 1)-paramete
 r family C of PCs of n intervals defined by an Iterated Function System {
 φ1\, . . . \, φn}. More specifically\, let φ1\, . . . \, φn : [0\, 1] 
 → (0\, 1) be a given collection of Lipschitz-continuous piecewise contra
 ctions. We prove that for Lebesgue almost every 0 = x0 &lt\; x1 &lt\; · 
 · · &lt\; xn−1 &lt\; xn = 1\, the PC of n intervals f : [0\, 1) → [0
 \, 1) defined by x ∈ [xi−1\, xi) → φi(x) has at least one and at mo
 st n periodic orbits. Besides\, the w-limit set of every point x ∈ [0\, 
 1) is a periodic orbit. Joint work with Arnaldo Nogueira and Rafael Rosale
 s.\nhttps://hal.archives-ouvertes.fr/hal-01341987\n\n&nbsp\;\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Benito_Pires.jpg
CATEGORIES:Séminaire,Ernest
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