Noncollision singularities in a planar 4-body problem

Noncollision Singularities in the Newtonian N-body Problem: Results and Perspectives

Noncollision Singularities: Do Four Bodies Suffice!

then we say that there is a collision between bodies i and j at t = t∗. Can there be a singularity without a collision? For example, Poincaré suggested, ri(t) might tend to infinity, or oscillate wildly (like sin 1 t ) as t→ t∗. Although Poincaré never wrote anything about noncollision singularities, Painlèvé gave him credit for being the first to ask this question. Painlèvé himself was able to...

Singularities in the Newtonian n-body Problem

In this note, we study the structure of singularities of the Newtonian n-body problem where we establish certain relations between collisions and noncollision singularities. Based on our results, we conjecture that the set of all accumulation points of collisions in the extended phase space is exactly the set of initial conditions that lead to a noncollision singularity.

Sequential Competitive Facility Location Problem in a Discrete Planar Space

In this paper, there are two competitors in a planar market. The first competitor, called, the leader, opens new facilities. After that, the second competitor, the follower, reacts to the leader’s action and opens r new facilities. The leader and the follower have got some facilities in advance in this market. The optimal locations for leader and follower are chosen among predefined candida...

A trial symbolic dynamics of the planar three - body problem

Symbolic dynamics is applied to the planar three-body problem. Symbols are defined on the planar orbit when it experiences a syzygy crossing. If the body i is in the middle at the syzygy crossing and the vectorial area of the triangle made with three bodies changes sign from + to −, number i is given to this event, whereas if the vectorial area changes sign from − to +, number i+3 is given. We ...