Smoothness in disjoint groups of real functions under composition.
Solution complète au problème de Siegel de linéarisation d'une application holomorphe au voisinage d'un point fixe
Solutions for the p-order Feigenbaum’s functional equation
This work deals with Feigenbaum’s functional equation ⎧ , ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 2 is an integer, is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [-1,1] with h(0) = 0 and |h(x)| < |x| (x ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.
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.
Solutions with big graph of iterative functional equations of higher orders
Solving some functional and operational equations.
Some aspects of the local theory of generalized Dhombres functional equations in the complex domain
We study the generalized Dhombres functional equation f(zf(z)) = ϕ(f(z)) in the complex domain. The function ϕ is given and we are looking for solutions f with f(0) = w0 and w0 is a primitive root of unity of order l ≥ 2. All formal solutions for this case are described in this work, for the situation where ϕ can be transformed into a function which is linearizable and local analytic in a neighbourhood of zero we also show...
Some continuity and approximation properties of a countable iterated function system.
Some functional inequalities and their Baire category properties.
Some functional inequalities and their Baire category properties. (Summary).
Some remarks on the general theorem of the existence of iterative roots of homeomorphisms with a rational rotation number
We show that the theorem proved in [8] generalises the previous results concerning orientation-preserving iterative roots of homeomorphisms of the circle with a rational rotation number (see [2], [6], [10] and [7]).
Stability of Jungck-type iterative procedures.
Stability of normal regions for linear homogenous functional equations.
Strictly decreasing solutions of a class of iterative equations on the unit circle.
Subgroups of the group Zn and a generalization of the Golab-Schinzel functional equation.
Substitution systems associated with the dynamical system (𝒜, Tf)*
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...
Sur la caractérisation de la fonction f(x) = x par des équations fonctionnelles, II. (Short Communication).
Sur les équations fonctionelles aux itérées.
Sur les équations fonctionelles aux q-différences.