Sala Conferenze (Puteano, Centro De Giorgi).<\/p>\n
We are interested in the asymptotical behavior of piecewise contractions of the interval (PCs). A map $f:[0,1)\\to [0,1)$ is an {\\it $n$ interval PC} if there exists a partition of the interval $[0,1)$ into subintervals $J_1,\\ldots,J_n$ such that each restriction $f\\vert_{J_\\ell}:J_\\ell \\to [0,1)$ is a Lipschitz-continuous contraction. Let $\\{\\phi_1,\\ldots,\\phi_n\\}$ be an Iterated Function System (IFS), where each $\\phi_\\ell:[0,1]\\to (0,1)$ is a Lipschitz-continuous contraction. Setting $x_0=0$ and $x_n=1$, we prove that for Lebesgue almost every $(n-1)$-dimensional point $(x_1,… ,x_{n-1})$ with $0 <\/p>\n","protected":false},"excerpt":{"rendered":"
We are interested in the asymptotical behavior of piecewise contractions of the interval (PCs). A map $f:[0,1)\\to [0,1)$ is an {\\it $n$ interval PC} if there exists a partition of the interval $[0,1)$ into subintervals $J_1,\\ldots,J_n$ such that…<\/p>\n