AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIAPAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN


The STUDIA UNIVERSITATIS BABEŞBOLYAI issue article summary The summary of the selected article appears at the bottom of the page. In order to get back to the contents of the issue this article belongs to you have to access the link from the title. In order to see all the articles of the archive which have as author/coauthor one of the authors mentioned below, you have to access the link from the author's name. 

STUDIA MATHEMATICA  Issue no. 2 / 2007  
Article: 
BOOK REVIEWS  K. BURNS AND M. GIDEA, DIFFERENTIAL GEOMETRY AND TOPOLOGY WITH A VIEW TO DYNAMICAL SYSTEMS, CHAPMAN & HALL/CRC (STUDIES IN ADVANCED MATHEMATICS), 2005, ISBN 1584882530, 9781584882534, HARDCOVER, IX+389 PP.. Authors: PAUL A. BLAGA. 

Abstract: This is a graduate course on the topology and differential geometry of smooth manifolds, introducing, in parallel, the basic notions of smooth dynamical systems. The first two chapters of the book introduce the basics of differential topology (manifolds and maps, the tangent bundle, immersions, submersions, embeddings, submanifolds, critical points, the Sard’s theorem) and vector fields and the associated dynamical systems. The following three chapters make up a concise introduction to Riemannian geometry, covering most of the standard material (Riemannian metrics, connections, geodesics, the exponential map, minimal geodesics, the Riemannian distance, Riemannian curvature, Riemannian submanifolds, sectional and Ricci curvature, Jacobi fields and conjugate points,manifolds of constant curvature). Chapter 6, Tensors and Differential Forms, is devoted, essentially, to integration theory of manifolds, as well to the de Rham cohomology. It is also, introduced the singular homology and it is given a proof of the de Rham theorem. Chapter 7 is concerned with some global results in the theory of smooth manifolds and Riemannian geometry (the Brouwer degree, the intersection number, the fixed point index, the Lefschetz number, the Euler characteristic and the GaussBonnet theorem), while the chapter 8 covers the basic notions and results of Morse theory. Finally, the chapter 9 provides a short introduction to the theory of hyperbolic dynamical systems.  