18 citations · 84 across the 20 of their papers we have counts for
4 papers · 1 filter
Almost everywhere balanced sequences of complexity
Julien Cassaigne, Sébastien Labbé, Julien Leroy
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 show that…
Arnoux-Rauzy interval exchange transformations
Pierre Arnoux, Julien Cassaigne, Sébastien Ferenczi +1
The Arnoux-Rauzy systems are defined in \cite{ar}, both as symbolic systems on three letters and exchanges of six intervals on the circle. In connection with a conjecture of S.P. N…
Outer billiard outside regular polygons
Nicolas Bedaride, Julien Cassaigne
We consider outer billiard outside regular convex polygons. We deal with the case of regular polygons with sides, and we describe the symbolic dynamics of the map…
Complexity and growth for polygonal billiards
J. Cassaigne, P. Hubert, S. Troubetzkoy
We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity funct…