Abstract
We study the relationship between transitivity and topological chaos for homeomorphisms of the two torus. We show that if a transitive homeomorphism of is homotopic to the identity and has both a fixed point and a periodic point which is not fixed, then it has a topological horseshoe. We also show that if a transitive homeomorphisms of is homotopic to a Dehn twist, then either it is aperiodic or it has a topological horseshoe.
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