A variational characterization of Einstein-Brillouin-Keller quantization

Abstract

In this paper we explain how to construct the EBK spectrum from the marked action spectrum and derive a minimax formula for concave toric domains. In the special case of the billiard on the disk we show that while the action spectrum is algebraic the EBK spectrum has infinite transcendence degree under the assumption that Schanuel's conjecture is true.