4 citations · 7 across the 6 of their papers we have counts for
12 papers · 1 filter
Orbit structure of interval exchange transformations with flip
Arnaldo Nogueira, Benito Pires, Serge Troubetzkoy
A sharp bound on the number of invariant components of an interval exchange transformation is provided. More precisely, it is proved that the number of periodic components n_per an…
Quantisations of piecewise affine maps on the torus and their quantum limits
Cheng-Hung Chang, Tyll Krueger, Roman Schubert +1
For general quantum systems the semiclassical behaviour of eigenfunctions in relation to the ergodic properties of the underlying classical system is quite difficult to understand.…
Dual billiards, Fagnano orbits and regular polygons
Serge Troubetzkoy
We study the notion of Fagnano orbits for dual polygonal billiards. We used them to characterize regular polygons and we study the iteration of the developing map.
Periodic billiard orbits in right triangles II
Serge Troubetzkoy
Periodic billiard orbits are dense in the phase space of an irrational right triangle. A stronger pointwise density result is also proven.
Periodic billiard orbits in right triangle
Serge Troubetzkoy
There is an open set of right triangles such that for each irrational triangle in this set (i) periodic billiards orbits are dense in the phase space, (ii) there is a unique nonsin…
Rotor interaction in the annulus billiard
Péter Bálint, Serge Troubetzkoy
Introducing the rotor interaction in the integrable system of the annulus billiard produces a variety of dynamical phenomena, from integrability to ergodicity.