Variation of Physical Measures in Nontrivial Mixed Partially Hyperbolic Systems

We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed points with mutually distinct unstable indices. By appropriately perturbing the skeleton, we provide an example where the number of physical measures varies upper semi-continuously. The general framework of mixed partially hyperbolic systems has been studied in theorem.