Abstract We study the ergodicity of partially hyperbolic endomorphisms, focusing on skew products whose base dynamics are governed by Anosov endomorphisms. For this family, we establish ergodicity and prove that accessibility holds on an open and dense subset. By analysing the topological implications of accessibility, we demonstrate that conservative accessible partially hyperbolic endomorphisms are topologically transitive. Leveraging accessibility, we further show ergodicity for skew products with S 1 -fibres. Finally, outside the context of rotation extensions, we prove ergodic stability results for partially hyperbolic endomorphisms with dim ( E c ) = 1.
Micena et al. (Thu,) studied this question.
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