A criterion for transitivity of area preserving partially hyperbolic endomorphism on torus

TL;DR

This paper introduces a new criterion called order-n transversality to determine the transitivity of area-preserving partially hyperbolic endomorphisms on the torus, addressing an open problem in the field.

Contribution

It proposes a novel transversality criterion for transitivity and provides an answer to Gan's problem related to these dynamical systems.

Findings

Established the order-n transversality criterion for transitivity.

Provided a solution to Gan's problem in the context of partially hyperbolic endomorphisms.

Enhanced understanding of the conditions for transitivity in area-preserving dynamical systems.

Abstract

We propose a criterion, referred to as order-n transversality, for transitivity of area preserving partially hyperbolic endomorphisms. Besides, we also give a further answer to the Gan's problem, as proposed in the work of Baolin He.