1994/06/30 by F. Christiansen, Freddy Christiansen, Hans Henrik Rugh +2 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum chaos and dynamical systems #chao-dyn #gr-qc #nlin.CD #nlin.SI #solv-int
paper · pdf · doi:10.1088/0305-4470/28/3/019
published as J.Phys. A28 (1995) 657-668 · 11 pages LaTeX in J.Phys.A style (ioplppt.sty) + 6 PostScript figures compressed and uuencoded with uufiles. Revised version to appear in J Phys. A
arxiv created 1994/12/18 · openalex publication_date 1995/02/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We comment on an analysis by Contopoulos et al.(1993) which demonstrates that the governing six-dimensional Einstein equations for the mixmaster spacetime metric pass the ARS or reduced Painleve test. We note that this is the case irrespective of the value, I, of the generating Hamiltonian which is a constant of motion. For I<0 we find numerous closed orbits with two unstable eigenvalues strongly indicating that two additional first integrals apart from the Hamiltonian cannot exist and thus that the system, at least for this case, is very probably not integrable. In addition, we present numerical evidence that the average Lyapunov exponent nevertheless vanishes. The model is thus a very interesting example of a Hamiltonian dynamical system, which is probably non-integrable yet passes the reduced Painleve test.