Desiderata
Biblioteche di Ateneo

Riferimento

To understand the general theory of dynamical systems and chaos, one needs to understand the concepts of modern differential geometry like manifolds, advanced understandings of vector fields (e.g. Lie derivatives), and differential forms. This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master’s students. It places special emphasis on motivation and understanding, while developing a solid intuition for the more abstract concepts. In contrast to graduate level references, the text relies on a minimal set of prerequisites: a solid grounding in linear algebra and multivariable calculus, and ideally a course on ordinary differential equations. Manifolds are introduced intrinsically in terms of coordinate patches glued by transition functions. The theory is presented as a natural continuation of multivariable calculus; the role of point-set topology is kept to a minimum.

s260250 AT studenti DOT polito DOT it