On non-elementary singular points

✍ Scribed by J.K. Aggarwal

• Book ID: 103086954
• Publisher: Elsevier Science
• Year: 1966
• Tongue: English
• Weight: 660 KB
• Volume: 281
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(66)90066-4

✦ Synopsis

ALBEITRACT: The varCous admissible conJigurations of trajectories near a singular point are fan, hyperbolic sector, elliptic sector, center and focus. Except for the elliptic sector all of these configurations occur in the linear case. The trajectories in the neighborhood of an isolated singularity, described by the equations .i: = ax" + by" and g = cx* + dy", have been examined and it is shown that the index for this singularity is +1 or -1 for n odd, and is zero for n even. Further, it is shown that indices of -1 and 0 and +l correspond to four, two and zero hyperbolic sectors, and that elliptical sectors do not occur for the class of singularities under consideration. The index of f 1 corresponds to a node, focus OT center. This shows that the qualitative behavior of trajectories in the neighborhood of singular point for n odd is similar to the linear case (n = 1).