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LION AND MAN GAME ON A COMPACT METRIC SPACE

Annotation

The lion and man game on a compact metric space is considered. Both players have the equal speeds. Suppose that 1) for all pairs of points there exists a unique geodesic connecting this points; 2) every geodesic continuously depends on its own endpoints. Then the strategy of simple pursuit guarantees the ε -capture. In particular, this implies the same result for CAT(0) domains.

Keywords

pursuit-evader game; Lion and Man; compact set; geodesic; metric spaces; simple pursuit strategy

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UDC

517.977

Pages

1546-1549

References

1. Alexander S., Bishop R., Ghrist R. Total curvature and simple pursuit on domains of curvature bounded above // Geometriae Dedicata. 2010. V. 149. № 1. P. 275–290. 2. Miroslav B. Note on a compactness characterization via a pursuit game // Geometriae Dedicata. 2012. V. 160. № 1. P. 195–197. 3. Noori N., Isler V. Lion and Man with Visibility in Monotone Polygons // The International Journal of Robotics Research. 2013. 4. Noori N., Isler V. The Lion and Man Game on Convex Terrains. 2014. 5. Bramson M., Burdzy K., Kendall W. Shy couplings, CAT(0) spaces, and the lion and man // Ann. Probab. 2013. V. 41. № 2. P. 744–784.

Received

2015-06-01

Section of issue

Scientific articles

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