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 some classes of dynamical systems, including partially hyperbolic diffeomorphisms and automorphisms of compact metric abelian groups with positive topological entropy, have semi-horseshoes. The versions for attractors and local $C^1$-diffeomorphisms of the above result are also obtained.

 

 

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