Marian Gidea, Clark Robinson Topologically crossing heteroclinic connections to invariant tori (664K, pdf) ABSTRACT. 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. Topological 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 Zgliczynski.