Non-Integrable Flat Dynamical Systems

The approach to addressing some of these uniformity questions combines traditional ergodic theory methods, such as the Birkhoff ergodic theorem, with tools from number theory and new ideas outside the field of ergodic theory. Several non-trivial results on 3-dimensional flat systems are included, expanding upon the extensive literature on 2-dimensional non-integrable flat dynamical systems, which often focuses on plane-specific methods that do not readily adapt to 3-dimensional systems. New approaches are developed to address these challenges.

A systematic study of a class of dissipative systems is also presented, where the flow is neither time-reversible nor measure-preserving. The overwhelming majority of the material in this book represents previously unpublished research.