A. Nogueira

activity

20102025

most citedDynamics of piecewise contractions of the interval

23 citations · 64 across the 18 of their papers we have counts for

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15 papers · 1 filter

math.DS2025

Rotation number and dynamics of 3-interval piecewise $λ$ -affine contractions

P. Guiraud, M. Hernández, A. Meyroneinc +1

We consider a family of piecewise contractions admitting a rotation number and defined for every $x \in [0, 1)$ by $f (x) = λ x + δ + d θ_{a} (x) (mod 1)$ , where $λ \in (0, 1)$ , $d \in (0, 1 - λ)$ , $…

math.DS2023

On the complexity of polygonal billiards

Tyll Krueger, Arnaldo Nogueira, Serge Troubetzkoy

We show that the complexity of the billiard in a typical polygon grows cubically and the number of saddle connections grows quadratically along certain subsequences. It is known th…

math.DS2022

Rotation number of 2-interval piecewise affine maps

José Pedro Gaivao, Michel Laurent, Arnaldo Nogueira

We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps $f_{\p}$ are parametrized by a quintupl…

math.DS2020

Chess Billiards

Arnaldo Nogueira, Serge Troubetzkoy

We show the chess billiard map, which was introduced in [HM] in order to study a generalization of the $n$ -Queens problem in chess, is a circle homeomorphism. We give a survey of s…

math.DS2020

Dynamics of piecewise increasing contractions

José Pedro Gaivão, Arnaldo Nogueira

Let $I_{1} = [a_{0}, a_{1}), \dots, I_{k} = [a_{k - 1}, a_{k})$ be a partition of the interval $I = [0, 1)$ into $k$ subintervals. Let $f : I \to I$ be a map such that each restriction $f ∣_{I_{i}}$ is an…

math.DS2019

Dynamics of 2-interval piecewise affine maps and Hecke-Mahler series

Michel Laurent, Arnaldo Nogueira

Let $f : [0, 1) \to [0, 1)$ be a $2$ -interval piecewise affine increasing map which is injective but not surjective. Such a map $f$ has a rotation number and can be parametriz…