In hyperbolic geometry, a horocycle (from Greek roots meaning "boundary circle"), sometimes called an oricycle or limit circle, is a curve of constant...

ideal point, the centre of the horocycle). Through every pair of points there are two horocycles. The centres of the horocycles are the ideal points of the...

boundary circle is not part of the horocycle. It is an ideal point and is the hyperbolic center of the horocycle. It is also the point to which all the...

to some given horocycle. These numbers are the hyperbolic distance x h {\displaystyle x_{h}} from P {\displaystyle P} to the horocycle, and the (signed)...

terms horosphere and horocycle are due to Lobachevsky, who established various results showing that the geometry of horocycles and the horosphere in...

mathematics, ergodic flows occur in geometry, through the geodesic and horocycle flows of closed hyperbolic surfaces. Both of these examples have been...

boundary circle are not distorted. All other circles are distorted, as are horocycles and hypercycles Chords that meet on the boundary circle are limiting parallel...

and information theory. He has published contributions in the theory of horocycle flows and entropy. Marcus has written over seventy research papers, some...

The half pseudosphere of curvature −1 is covered by the interior of a horocycle. In the Poincaré half-plane model one convenient choice is the portion...

given point that share a tangent through that point converge towards a horocycle as their distances go towards infinity. Hypercycles in hyperbolic geometry...