Dimension Estimates in Smooth Dynamics: a Survey

  title={Dimension Estimates in Smooth Dynamics: a Survey},
  author={Lu{\'i}s Barreira and Katrin Gelfert},
We survey a collection of results in the dimension theory of dynamical systems, with emphasis on the study of repellers and hyperbolic sets of smooth dynamics. We discuss the most preeminent results in the area as well as the main difficulties in developing a general theory. Despite many interesting and nontrivial developments, only the case of conformal dynamics is completely understood. On the other hand, the study of the dimension of invariant sets of nonconformal maps unveiled several new… CONTINUE READING