Resumen de Filling Times for Linear Flow on the Torus with Truncated Diophantine Conditions: A Brief Review and New Proof

H. Scott Dumas, Stéphane Fischler

• We show that the geometry-of-numbers method used by A. Bounemoura to obtain filling times for linear flow on the torus satisfying Diophantine conditions may be extended to the case of linear flow with truncated Diophantine conditions, and we use these methods to recover the optimal estimate first obtained by M. Berti, L. Biasco, and P. Bolle in 2003. We also briefly review the dynamics of linear flow on the torus, previous results, optimality, and applications of these estimates.