arXiv subjects

Magali Jay

Publications and source records attributed to Magali Jay.

3 recordsLinked to original sources

arXiv2026

Wind-tree tiling billiards and their trapping strips

We introduce a new dynamical system: the wind-tree tiling billiards. This system studies trajectories of a ray in Euclidean space which has a negative refractive index when encountering rectangular obstacles located at lattice points. We show that for almost every configuration of the system, trajectories with initial vertical direction are trapped in an infinite strip of the plane. This result is reminiscent of the propagation of light rays in Eaton lenses, as shown by Fr\k{a}czek and Schmoll.

math.DS↗

arXiv2024

Deviations for generalized tiling billiards in cyclic polygons

This work continues the study of tiling billiards, a class of dynamical system introduced by Davis et al. in 2018. We develop the study of generalized tiling billiards in a cyclic polygon. This work shows that the behavior of generalized tiling billiards in cyclic N-gons with N > 4 is considerably different from that of triangular and quadrilateral tiling billiards studied before. Indeed, we exhibit an open set of generalized tiling billiard trajectories deviating sublinearly from their asymptotic direction, whereas for N = 3 or 4 almost every trajectory stays at a bounded distance from a line. Moreover, we establish the rate of deviations both in the generic case and in some non generic cases.

math.DS↗

arXiv2022

Relations with a fixed interval exchange transformation

We study the group of all interval exchange transformations (IETs). We show that for every IET $S$, there exists a dense open set of admissible IETs that share a relation with $S$. This is an extension of a result published by Dahmani, Fujiwara and Guirardel in 2013: the group generated by a generic pair of elements of IET([0;1[) is not free (assuming a suitable condition on the underlying permutation). Key words: interval exchange transformations, free group of rank 2, interval exchange transformations with flips.

math.GR↗