Billiards with countably many scatterers under no eclipse
Volume 265 / 2024
Fundamenta Mathematicae 265 (2024), 165-177
MSC: Primary 37C83; Secondary 37C30, 37B10
DOI: 10.4064/fm230728-23-1
Published online: 4 March 2024
Abstract
We consider a billiard flow with countably infinitely many scatterers on the plane without eclipse. We show that the non-wandering set of the billiard flow is in one-to-one correspondence with a two-sided topological Markov shift with countably many states. We also give a sufficient condition for the Euler product formula for the zeta function with respect to the billiard flow.
