Nonlinear analysis methods applied in celestial mechanics.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1028.70001
publication date: 2001-12-02T00:00:00Z
Mathematics Subject Classification ID: 70-02
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 70F17
Mathematics Subject Classification ID: 70F10
zbMATH DE Number: 1678118
zbMATH Keywords: \(N\)-body problem
zbMATH Keywords: Legendre transform
zbMATH Keywords: fixed point theorems
zbMATH Keywords: topological degree
zbMATH Keywords: periodic solution
zbMATH Keywords: restricted three-body problem
zbMATH Keywords: photo-gravitational effect
zbMATH Keywords: existence of periodic solutions
zbMATH Keywords: inverse problem
zbMATH Keywords: non-conservative systems
zbMATH Keywords: rotating frames
author: Mira-Cristiana Anisiu
MaRDI profile type: Publication
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title: Nonlinear analysis methods applied in celestial mechanics.
review text: The book under review is the author's thesis held at the Faculty of Mathematics and Informatics of ``Babeş-Bolyai'' University, Cluj-Napoca, Romania. NEWLINENEWLINENEWLINEThe first chapter contains some classical fixed point theorems and a generalization, due to the author, of the classical theorem of Schönberg, Singh, Massa and Roux. This chapter also presents the notion of topological degree, some variational problems, and mathematical models of certain problems of celestial mechanics: the \(N\)-body problem, and the restricted three-body problem with photo-gravitational effect. In the second chapter, the Legendre transform is treated following the paper by \textit{A. Pal} and \textit{M.-C. Anisiu} [Stud. Univ. Babeş-Bolyai, Math. 40, No. 2, 75-99 (1995; Zbl 0878.70011)]. NEWLINENEWLINENEWLINEIn chapter 3, the author presents fixed point methods (one using the topological degree and a variational one) of proving existence of periodic solutions for differential equations. These methods are used in chapter 4 where some periodic solutions are given to the plane restricted three-body problem. All these results are used in the fifth chapter which treats the inverse problems of dynamics: known a given family of orbits of a dynamical system, find the field which produces the motion of the system. The author presents some of her results concerning the inverse problem for non-conservative systems in rotating frames, published in joint works with A. Pal and G. Bozis: \textit{M.-C.~Anisiu} and \textit{A. Pal} [Astron. Nachr. 317, 205-209 (1996; Zbl 0858.70007)], and \textit{M.-C. Anisiu} and \textit{G.~Bozis} [Rom. Astron. J. 6, 42-52 (1996)].
reviewed by: Ingrid Beltiţă
description: scientific article; zbMATH DE number 1678118