A cusp closing theorem

A Cusp Slope-central Anisotropy Theorem

For a wide class of self-gravitating systems, we show that if the density is cusped like r −γ near the center, then the limiting value of the anisotropy parameter β = 1 − v 2 T /(2v 2 r) at the center may not be greater than γ/2. Here, v 2 r and v 2 T are the radial and tangential velocity second moments. This follows from the non-negativity of the phase space density. We compare this theorem t...

Billiards inside a Cusp

A cusp catastrophe model

A cusp catastrophe model Y. Xiao et al.

A GENERALIZATION OF A JACOBSON’S COMMUTATIVITY THEOREM

In this paper we study the structure and the commutativity of a ring R, in which for each x,y ? R, there exist two integers depending on x,y such that [x,y]k equals x n or y n.

A Cusp Slope - Central Anisotropy

For a wide class of self-gravitating systems, we show that if the density is cusped like r −γ near the center, then the limiting value of the anisotropy parameter β = 1 − v 2 T /(2v 2 r) at the center may not be greater than γ/2. Here, v 2 r and v 2 T are the radial and tangential velocity second moments. This follows from the non-negativity of the phase space density. We compare this theorem t...