Ergodic theory for smooth one-dimensional dynamical systems

摘要

In this paper we study measurable dynamics for the widest reasonable class ofsmooth one dimensional maps. Three principle decompositions are described inthis class : decomposition of the global measure-theoretical attractor intoprimitive ones, ergodic decomposition and Hopf decomposition. For maps withnegative Schwarzian derivative this was done in the series of papers [BL1-BL5],but the approach to the general smooth case must be different.