We propose a new point of view on multidimensional continued fraction algorithms inspired
by Rauzy induction. The generic behaviour of such an algorithm is described here as a …

We first survey the current state of the art concerning the dynamical properties of
multidimensional continued fraction algorithms defined dynamically as piecewise fractional …

We study the strong convergence of certain multidimensional continued fraction algorithms.
In particular, in the two-and three-dimensional case, we prove that the second Lyapunov …

We study ternary sequences associated with a multidimensional continued fraction
algorithm introduced by the first author. The algorithm is defined by two matrices and we …

AS Skripchenko, “Renormalization in one-dimensional dynamics”, Uspekhi Mat. Nauk, 78:6(474)
(2023), 3–46; Russian Math. Surveys, 78:6 (2023), 983–1021 Russian Mathematical Surveys …

We study the complexity of S-adic sequences corresponding to a family of 216 multi-
dimensional continued fractions maps, called Triangle Partition maps (TRIP maps), with an …

We study a class of interval translation mappings introduced by Bruin and Troubetzkoy,
describing a new renormalization scheme, inspired by the classical Rauzy induction for this …

Our goal is to show that the additive-slow-Farey version of the Triangle map (a type of
multidimensional continued fraction algorithm) gives us a method for producing a map from …

Изучение динамических и топологических свойств перекладываний отрезков и их
естественных обобщений является важной задачей, находящейся на стыке нескольких …

Triangle partition maps form a family that includes many, if not most, well-known
multidimensional continued fraction algorithms. This paper begins the exploration of the …