Marian Gidea, Clark Robinson
Shadowing orbits for transition chains of invariant tori alternating with Birkhoff zones of instability
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ABSTRACT.  We consider a dynamical system that exhibits transition chains of 
invariant tori alternating with Birkhoff zones of instability in a 
$2$-dimensional center manifold. It is known that there exist 
orbits that shadow the transition chains. It is also known that 
there exist orbits that cross the Birkhoff zones of instability. 
We describe a topological mechanism that allows one to join 
together the two types of orbits. We prove the existence of 
diffusing orbits that shadow the transition chains of invariant 
tori and cross the Birkhoff zones of instability. This approach is 
motivated by what has been called the large gap problem in 
Hamiltonian systems.