Horocyclic flow

cjerdonek authored on Nov. 8, 2020, 12:57 a.m.

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In hyperbolic geometry, the horocyclic flow on a hyperbolic surface is a canonical flow on the unit tangent bundle of the surface that moves tangent vectors sideways along the horocycle centered in the tangent vector's direction.	In hyperbolic geometry, the horocyclic flow on a hyperbolic surface is a canonical flow on the unit tangent bundle of the surface that moves tangent vectors sideways along the horocycle centered in the tangent vector's direction. This figure illustrates the horocyclic flow in the Poincaré disk model of the hyperbolic plane. The figure shows the flow restricted to the subspace of unit tangent vectors that point to the boundary point at the top (i.e. the complex point \(i\) in the disk model). This subspace is a section of the unit tangent bundle of the plane and is preserved by the flow.

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In hyperbolic geometry, the horocyclic flow on a hyperbolic surface is a canonical flow on the unit tangent bundle of the surface that moves tangent vectors sideways along the horocycle centered in the tangent vector's direction.

This figure illustrates the horocyclic flow in the Poincaré disk model of the hyperbolic plane. The figure shows the flow restricted to the subspace of unit tangent vectors that point to the boundary point at the top (i.e. the complex point \(i\) in the disk model). This subspace is a section of the unit tangent bundle of the plane and is preserved by the flow.

cjerdonek / Horocyclic flow 1e8bcbe36c786fe30fa043e324737bd4e09ae23a