The existence of semi-horseshoes for partially hyperbolic diffeomorphisms

Abstract A topological dynamical system is said to have a semi-horseshoe if there exists a subsystem of its iterates which is topologically semi-conjugate to the full shift. It is shown that several classes of dynamical systems, including partially hyperbolic diffeomorphisms and automorphisms of compact metric abelian groups with positive topological entropy, have semi-horseshoes.

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