- 03-99 Marian Gidea, Clark Robinson
- Topologically crossing heteroclinic connections to invariant tori
Mar 9, 03
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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.