On the Problem of Infinite Spin in Total Collisions of the Planar $n$-body Problem (Memoirs of the American Mathematical Society, 304) - Softcover

Yu, Xiang

 
9781470472498: On the Problem of Infinite Spin in Total Collisions of the Planar $n$-body Problem (Memoirs of the American Mathematical Society, 304)
Softcover
ISBN 10: 147047249X ISBN 13: 9781470472498
Verlag: American Mathematical Society, 2025

Inhaltsangabe

"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 casecorresponding 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 furtheranswer 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"-- Provided by publisher.

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Über die Autorin bzw. den Autor

Xiang Yu, Tianjin University, People's Republic of China, and Southwestern University of Finance and Economics, Chengdu, People's Republic of China.

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Verlag
American Mathematical Society
Erscheinungsdatum
2025
Sprache
Englisch
ISBN 10 
147047249X
ISBN 13 
9781470472498
Einband
Taschenbuch
Anzahl der Seiten
82
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
preigu
mail@preigu.de

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