The aim of the paper is to give a survey of results concerning iterations in rings of formal
power series in one indeterminate. We characterize the algebraic structure of groups and …

We study the algebraic structure of the groups of solutions of the third Acz {\'e} l-Jabotinsky
differential equation $(H\circ\Phi)(x)=\frac {d\Phi}{dx}\cdot H (x) $ in the rings of formal power …

We investigate the translation equation F (s+ t, x)= F (s, F (t, x)),\quad\quad s, t ∈
C,\qquad\qquad\qquad\qquad (\rm T) in C\left\kern-0.15 em\left x\right\kern-0.15 em\right …

Let L s 1 (s∈ ℕ) be the s-th differential group, that is the set {(x1,…, xs): x 1≠ 0, xn∈ K, n= 1,
2,…, s}(K∈{ℝ, ℂ}) together with the group operation which describes the chain rules (up to …

The aim of the paper is to describe one-parameter groups of formal power series, that is to
find a general form of all homomorphisms\Theta_G: G → Γ Θ G: G→ Γ,\Theta_G (t)= k= 1^ ∞ …

We prove in this paper that stability of the translation equation in the ring of formal power
series KΩΩXää (more precisely, in the group of invertible formal series over K) is equivalent …

In this paper we describe families of commuting invertible formal power series in one
indeterminate over C, using the method of formal functional equations. We give a …

The aim of the paper is to give a survey of results and open problems concerning one-
parameter groups of formal power series in one indeterminate. A one-parameter group of …

In this survey we describe the construction of one-parameter subgroups (iteration groups) of
Γ, the group of all (with respect to substitution) invertible power series in one indeterminate x …

2.2. Historical sources for the functional equation (LG) 5 2.3. Properties of bijective solutions
of (LG) 9 2.4. Solving (LG) by a physicist's approach 10 2.5. Algebraic and transcendental …