Custom cover image
Custom cover image

On the problem of infinite spin in total collisions of the planar N-body problem / Xiang Yu

By: Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 304, number 1532 (December 2024)Publisher: Providence, RI : American Mathematical Society, December 2024Description: v, 82 SeitenISBN:
  • 9781470472498
Subject(s): Additional physical formats: Erscheint auch als: On the problem of infinite spin in total collisions of the planar N-body problem. Online-Ausgabe Providence, RI : American Mathematical Society, 2024. 1 Online-Ressource (v, 82 Seiten)MSC: MSC: 70F10 | 70F16 | 34A34 | 70F15RVK: RVK: SI 130Summary: For the planar N-body problem, we introduce a class of moving coordinates suitable for orbits near central configurations, especially for total collision orbits, which is the main new ingredient of this paper. The moving coordinates allow us to reduce the degeneracy of the N-Body problem from its intrinsic symmetrical characteristic. First, we give a full answer to the infinite spin or Painleve´−Wintner problem in the case corresponding to nondegenerate central configurations. Then following some original ideas of C.L. Siegel, especially the idea of normal forms, and applying the theory of central manifolds, we give a partial answer to the problem {in the case corresponding to} degenerate central configurations. We completely answer the problem {in the case corresponding to} central configurations with degree of degeneracy one. Combining some results on the planar nonhyperbolic equilibrium point, we give a criterion {in the case corresponding to} central configurations with degree of degeneracy two. We further answer the problem {in the case corresponding to} all known central configurations of four bodies. Therefore, we solve the problem for almost every choice of the masses of the four-body problem. Finally, we give a measure of the set of initial conditions leading to total collisions.Summary: Keywords: N-body problem; collisions; infinite spin; central configurations; Painleve´−Wintner problem; moving frame; normal forms; central manifoldsPPN: PPN: 1916007562
Holdings
Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c-304.2024,1532 Nicht ausleihbar
Total holds: 0
KIT – The Research University in the Helmholtz Association                         Home | Impressum | Datenschutz | Barrierefreiheit | KIT