Topologically crossing heteroclinic connections to invariant tori

We consider transition tori of Arnold which have topologically crossing heteroclinic connections. We prove the existence of shadowing orbits to a bi-infinite sequence of tori, and of symbolic dynamics near a finite collection of tori. Topologically crossing intersections of stable and unstable manifolds of tori can be found as non-trivial zeroes of certain Melnikov functions. Our treatment relies on an extension of Easton's method of correctly aligned windows due to Zgliczyński.