Splitting time for irrational triangle billiards
Dmitri Scheglov
TL;DR
This paper provides an upper estimate for the splitting time of a thin beam in irrational triangle billiards, linking it to number-theoretic functions of the angles, and offers specific bounds for certain angle classes.
Contribution
It introduces a novel upper estimate for splitting time in irrational triangle billiards based on number-theoretic properties of angles, with explicit bounds for particular angle classes.
Findings
Upper estimate for splitting time in irrational triangle billiards
Connection between splitting time and number-theoretic functions of angles
Explicit bounds for specific classes of angles
Abstract
We find an upper estimate for a splitting time of a thin parallel beam for irrational triangle billiards in terms of some number-theoretic function of angles. We provide an upper estimate on this function for some class of angles.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems