Smooth Cantor functions
We characterise the set on which an infinitely differentiable function can be locally polynomial.
Solutions with big graph of iterative functional equations of the second order.
Solutions with big graph of iterative functional equations of the first order
We obtain a result on the existence of a solution with big graph of functional equations of the form g(x,𝜑(x),𝜑(f(x)))=0 and we show that it is applicable to some important equations, both linear and nonlinear, including those of Abel, Böttcher and Schröder. The graph of such a solution 𝜑 has some strange properties: it is dense and connected, has full outer measure and is topologically big.
Sur une courbe, qui remplit toute une aire plane