{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T13:37:18Z","timestamp":1774877838269,"version":"3.50.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2011,8]]},"abstract":"<jats:p> We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits from stability to complex instability (also known as Hamiltonian Hopf Bifurcation) the four eigenvalues of the stable periodic orbits move out of the unit circle. Then the periodic orbits become complex unstable. In this paper, we first integrate initial conditions close to the ones of a complex unstable periodic orbit, which is close to the transition point. Then, we plot the consequents of the corresponding orbit in a 4D surface of section. To visualize this surface of section we use the method of color and rotation [Patsis &amp; Zachilas, 1994]. We find that the consequents are contained in 2D \"confined tori\". Then, we investigate the structure of the phase space in the neighborhood of complex unstable periodic orbits, which are further away from the transition point. In these cases we observe clouds of points in the 4D surfaces of section. The transition between the two types of orbital behavior is abrupt. <\/jats:p>","DOI":"10.1142\/s0218127411029811","type":"journal-article","created":{"date-parts":[[2011,7,8]],"date-time":"2011-07-08T14:14:41Z","timestamp":1310134481000},"page":"2321-2330","source":"Crossref","is-referenced-by-count":26,"title":["THE STRUCTURE AND EVOLUTION OF CONFINED TORI NEAR A HAMILTONIAN HOPF BIFURCATION"],"prefix":"10.1142","volume":"21","author":[{"given":"M.","family":"KATSANIKAS","sequence":"first","affiliation":[{"name":"Research Center for Astronomy, Academy of Athens, Soranou Efessiou 4, GR-11527 Athens, Greece"},{"name":"Section of Astrophysics, Astronomy and Mechanics, Department of Physics, University of Athens, Greece"}]},{"given":"P. A.","family":"PATSIS","sequence":"additional","affiliation":[{"name":"Research Center for Astronomy, Academy of Athens, Soranou Efessiou 4, GR-11527 Athens, Greece"}]},{"given":"G.","family":"CONTOPOULOS","sequence":"additional","affiliation":[{"name":"Research Center for Astronomy, Academy of Athens, Soranou Efessiou 4, GR-11527 Athens, Greece"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"61","volume":"4","author":"Bridges T. J.","journal-title":"Fields Inst. Comm."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/20\/2\/009"},{"key":"rf4","first-page":"33","volume":"92","author":"Contopoulos G.","journal-title":"Astron. Astrophys."},{"key":"rf5","first-page":"44","volume":"153","author":"Contopoulos G.","journal-title":"Astron. 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