Nonlinear analysis methods applied in celestial mechanics.
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)].
scientific article; zbMATH DE number 1678118