Markov spectra for modular billiards

TL;DR

This paper explores analogues of the Markov spectrum in the context of modular billiards, aiming to characterize the spectrum segment below its lowest limit point.

Contribution

It introduces new analogues of the Markov spectrum related to modular billiards and investigates their properties.

Findings

Identification of the spectrum segment below the lowest limit point.

New characterizations of the Markov spectrum analogues.

Insights into the structure of modular billiards spectra.

Abstract

We introduce some analogues of the Markov spectrum defined in terms of modular billiards and consider the problem of characterizing that part of the spectrum below the lowest limit point.