Search Theory

5Search Plans Generated by Billiards

DAVID V. CHUDNOVSKY AND GREGORY V. CHUDNOVSKY / Department of Mathematics, Columbia Univesity, New York, New York

DOI: 10.1201/9781003420057-5

1. INTRODUCTION

In an attempt to construct search trajectories (plans) for detection of immobile and movable targets in various domains, we are looking at dynamical systems with ergodic properties that generate ε-covering curves (tours or ε-Peano curves [1]) in a simple way. Billiards in rectangular domains are analyzed in terms of number-theoretic properties associated with the Weyl uniform distribution theorem. Alternative randomized strategy (particularly multiball billiards or “random pinball machines”) are suggested.

2. SEARCH GAMES FOR IMMOBILE AND MOVABLE ...