Dimension theory in non-conformal smooth systems

Compared with the relatively complete dimension theory established in conformal smooth dynamical systems, i.e., the Bowen equation and the variational principle of dimension, it still lacks today a satisfactory general approach for the dimension theory in non-conformal smooth dynamical systems. In this paper, we survey the recent results in the dimension theory of non-conformal smooth dynamical systems, including the dimension of repellers and hyperbolic sets of smooth maps as well as the dimension of measures supported on these invariant sets, and especially including the Bowen equation, the existence of measures of maximal or full dimension and dimension approximation.