Dynamical Cusp Regeneration

Dynamical Cusp Regeneration

After being destroyed by a binary supermassive black hole, a stellar density cusp can regrow at the center of a galaxy via energy exchange between stars moving in the gravitational field of the single, coalesced hole. We illustrate this process via high-accuracy N-body simulations. Regeneration requires roughly one relaxation time and the new cusp extends to a distance of roughly one-fifth the ...

Cusp algebras

By a cusp V we shall mean the image of the unit disk D under a bounded injective holomorphic map h into C whose derivative vanishes at exactly one point. The simplest example is the Neil parabola, given by h(ζ) = (ζ, ζ). See [3, 4] for background and theory on the Neil parabola, which is pictured in Figure 1. A generalization of a cusp is a petal. A petal is the image of the unit disk D under a...

Unfolding the Cusp-Cusp Bifurcation of Planar Endomorphisms

Abstract. In many applications of practical interest, for example, in control theory, economics, electronics and neural networks, the dynamics of the system under consideration can be modelled by an endomorphism, which is a discrete smooth map that does not have a uniquely defined inverse; one also speaks simply of a noninvertible map. In contrast to the better known case of a dynamical system ...

Billiards inside a Cusp

A cusp catastrophe model

A cusp catastrophe model Y. Xiao et al.