New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years,
gave deep insight into the dynamics of convex Lagrangian systems. This book shows how …

1. The language of Symplectic geometry is successfully employed in many branches of
contemporary mathematics, but it is worth to remind that the original development of …

This is an intuitively motivated presentation of many topics in classical mechanics and
related areas of control theory and calculus of variations. All topics throughout the book are …

In the case of completely integrable systems, periodic solutions are found by inspection. For
nonintegrable systems, such as the three-body problem in celestial mechanics, they are …

An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the
Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the …

John Mather's seminal works in Hamiltonian dynamics represent some of the most important
contributions to our understanding of the complex balance between stable and unstable …

These notes are based on the mini-course given in June 2004 in Cetraro, Italy, in the frame
of a CIME school. Of course, they contain much more material that I could present in the 6 h …

A geometric setting for the Pontryagin maximum principle in optimal control theory is
provided. The equations for critical trajectories are given in terms of a symplectic equation …

This essay highlights the contributions of geometric control theory to the calculus of
variations. The Maximum Principle is recognized as a covariant necessary condition of …

The author considers dynamical systems generated by time-dependent periodic
Lagrangians on a closed manifold M. An invariant probability mu of such a system has an …