We will study the
following concepts: diffeomorphisms and flows on manifolds, ergodic
theory, stable manifolds, structural stability. In this course, a
dynamical system is either a (invertible or noninvertible) map f : X →
X or a ﬂow (or semiﬂow) f(t): X → X.
The type of a dynamical system is determined by the structure of the
space X (then f should preserve that structure):
topological, measure theoretical, smooth, holomorphic, etc. And we
focus on the smooth case, so X = M is a manifold, and f is sufficiently
smooth.
Textbooks:
Anatole Katok and Boris Hasselblatt,
Introduction to the Modern Theory of Dynamical Systems, Cambridge
University Press.
Michael Brin and Garrett Stuck, Introduction to dynamical systems,
Cambridge University Press.
