Chaotic orbits obeying one isolating integral in a four dimensional map
  We have recently presented strong evidence that chaotic orbits that obey one
isolating integral besides energy exist in a toy Hamiltonian model with three
degrees of freedom and are bounded by regular orbits that isolate them from the
Arnold web. The interval covered by those numerical experiments was equivalent
to about one million Hubble times in a galactic context. Here we use a four
dimensional map to confirm our previous results and to extend that interval
fifty times. We show that, at least within that interval, features found in
lower dimension Hamiltonian systems and maps are also present in our study,
e.g., within the phase space occupied by a chaotic orbit that obeys one
integral there are subspaces where that orbit does not enter and are, instead,
occupied by regular orbits that, if tori, bound other chaotic orbits obeying
one integral and, if cantori, produce stickiness. We argue that the validity of
our results might exceed the time intervals covered by the numerical
experiments.
