Chaotic orbits obeying one isolating integral in a four-dimensional map

MUZZIO, J. C.

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY

WILEY-BLACKWELL PUBLISHING, INC

Año: 2018 vol. 473 p. 4636 - 4643

0035-8711

pre.cjk { font-family: "Nimbus Mono L", monospace; }p { margin-bottom: 0.1in; line-height: 120%; }a:link { }We have recently presented strong evidence that chaotic orbitsthat obey one isolating integral besides energy exist in a toyHamiltonian model with three degrees of freedom and are boundedby regular orbits that isolate them from the Arnold web. Theinterval covered by those numerical experiments was equivalentto about one million Hubble times in a galactic context. Here weuse a four dimensional map to confirm our previous results andto extend that interval fifty times. We show that, at leastwithin that interval, features found in lower dimensionHamiltonian systems and maps are also present in our study,e.g., within the phase space occupied by a chaotic orbit thatobeys one integral there are subspaces where that orbit doesnot enter and are, instead, occupied by regular orbits that, iftori, bound other chaotic orbits obeying one integral and, ifcantori, produce stickiness. We argue that the validity of ourresults might exceed the time intervals covered by the numericalexperiments.