This book consists of a presentation of the transversality theory and some of its applications to differentiable dynamical systems. Through a systematic use of transversality, the authors give a detailed proof of an important approximation theorem of I. Kupka Contributions to Differential Equations 2 (1963), 457--484; MR0165536 (29 #2818a) and S. Smale Ann. Scuola Norm. Sup. Pisa (3) 17 (1963), 97--116; MR0165537 (29 #2818b) for ; ^ ; vector fields on a compact manifold, ; geq ; From the authors' preface: The method used here to prove the Kupka-Smale theorem is a general technique for establishing generic properties of vector fields, mappings, partial differential equations, and so on. Here, the word generic has the following precise meaning: a generic property in a Baire space is a property common to all elements of this space, except for a subset of first category.
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The book is well written and self-contained. It is a very good introduction to global analysis for students with some background in differential topology and calculus in Banach spaces. For mathematicians interested in the subject it is certainly an excellent reference