4 citations · 6 across the 3 of their papers we have counts for
6 papers
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.
The Gauss map on a class of interval translation mappings
H. Bruin, S. Troubetzkoy
We study the dynamics of a class of interval translation map on three intervals. We show that in this class the typical ITM is of finite type (reduce to an interval exchange transf…
Central symmetries of periodic billiard orbits in right triangles
S. Troubetzkoy
This paper had a serious error. In fixing the error the emphasis of the paper has changed completely, thus meriting a new name: ``Periodic orbits in right triangles''. I have made…
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…
Topological and Symbolic Dynamics for Axiom A Diffeomorphisms with Holes
S. Bundfuss, T. Krueger, S. Troubetzkoy
We consider an Axiom A diffeomorphism and the invariant set of orbits which never falls into a fixed hole. We study various aspects of the complexity of the symbolic representa…
Return time statistics via inducing
Henk Bruin, Benoit Saussol, Serge Troubetzkoy +1
We prove that return time statistics of a dynamical system do not change if one passes to an induced (i.e. first return) map. We apply this to show exponential return time statisti…