Fetching the paper…
Reading the bibliography…
We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a general relativistic system).
Kerr, R. P.: Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics. Phys. Rev. Lett. 11, 237-238 (1963). doi:10.1103/PhysRevLett.11.237
1963
Earlier work this paper cites.
Szebehely, V.: Theory of Orbits. Academic Press, New York (1967)
1967
Earlier work this paper cites.
Carter, B.: Global Structure of the Kerr Family of Gravitational Fields. Phys. Rev. 174, 1559-1571 (1968). doi:10.1103/PhysRev.174.1559
1968
Earlier work this paper cites.
Churchill, R., Pecelli, G., Rod, D.: Isolated unstable periodic orbits. J. Differ. Equ. 17, 329-348 (1975). doi:10.1016/0022-0396(75)90047-9
1975
Earlier work this paper cites.
Newhouse, S.E.: Quasi-elliptic periodic points in conservative dynamical systems. Am. J. Math. 99, 1061-1087 (1977)
1977
Earlier work this paper cites.
Contopoulos, G., Zikides, M.: Periodic orbits and ergodic components of a resonant dynamical system. Astron. Astrophys. 90, 198-203 (1980)
1980
Earlier work this paper cites.
Eckmann, J.-P.: Roads to turbulence in dissipative dynamical systems. Rev. Mod. Phys. 53, 643-654 (1981). doi:10.1103/RevModPhys.53.643
1981
Earlier work this paper cites.
Heggie, D. C.: On the bifurcations of a certain family of periodic orbits. Celest. Mech. Dyn. Astron. 29, 207-214 (1983). doi:10.1007/BF01229135
1983
Earlier work this paper cites.
Newhouse, S. E.: The creation of non-trivial recurrence in the dynamics of diffeomorphisms. In: Iooss, G., Helleman, R. H. G., Stora, R. (eds.) Chaotic Behaviour of Deterministic Systems, pp. 381–442. North-Holland, Amsterdam (1983)
1983
Earlier work this paper cites.
Petit, J.-M., Hénon, M.: Satellite encounters. Icarus 66, 536-555 (1986). doi:10.1016/0019-1035(86)90089-8
1986
Earlier work this paper cites.
Bleher, S. , Grebogi, C., Ott, E., Brown, R.: Fractal boundaries for exit in Hamiltonian dynamics. Phys. Rev. A 38, 930-938 (1988). doi:10.1103/PhysRevA.38.930
1988
Earlier work this paper cites.
Eckhardt, B.: Irregular scattering. Phys. D 33, 89-98 (1988). doi:10.1016/S0167-2789(98)90012-4
1988
Earlier work this paper cites.
Jung, C., Scholz, H.: Cantor set structures in the singularities of classical potential scattering. J. Phys. A 21, 3607-3617 (1988). doi:10.1088/0305-4470/20/12/015
1988
Earlier work this paper cites.
Hénon, M.: La diffusion chaotique. Rech. 209, 490-498 (1989)
1989
Cited alongside, same era.
Contopoulos, G.: Asymptotic curves and escapes in Hamiltonian systems. Astron. Astrophys. 231, 41-55 (1990)
1990
Cited alongside, same era.
Contopoulos, G., Kaufmann, D.: Types of escapes in a simple Hamiltonian system. Astron. Astrophys. 253, 379-388 (1992)
1992
Cited alongside, same era.
Manko, V. S., Novikov, I. D.: Generalizations of the Kerr and Kerr-Newman metrics possessing an arbitrary set of mass-multipole moments. Class. Quantum Gravity 9, 2477-2487 (1992). doi:10.1088/0264-9381/9/11/013
1992
Cited alongside, same era.
Contopoulos, G., Kandrup, H. E., Kaufmann D.: Fractal properties of escape from a two-dimensional potential. Phys. D 64, 310 (1993). doi:10.1016/0167-2789(93)90262-Y
1993
Cited alongside, same era.
Contopoulos, G.: Order and chaos in dynamical astronomy. Springer, Berlin (2002)
2002
Later among the works it cites.
Contopoulos, G., Efstathiou, K.: Escapes and Recurrence in a Simple Hamiltonian System. Celest. Mech. Dyn. Astron. 88, 163-183 (2004). doi:10.1023/B:CELE.0000016816.87061.11
2004
Later among the works it cites.
Contopoulos, G., Harsoula, M.: Stickiness in Chaos. Int. J. Bifurc. Chaos 18, 2929 (2008). doi:10.1142/S0218127408022172
2008
Later among the works it cites.
Cristadoro, G., Ketzmerick R.: Universality of Algebraic Decays in Hamiltonian Systems. Phys. Rev. Lett. 100, 184101 (2008). doi:10.1103/PhysRevLett.100.184101
2008
Later among the works it cites.
Gair, J. R., Li, C., Mandel, I.: Observable properties of orbits in exact bumpy spacetimes. Phys. Rev. D 77, 024035 (2008). doi:10.1103/PhysRevD.77.024035
2008
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Ott, E., Tél, T.: Chaotic scattering: An introduction. Chaos 3, 417-426 (1993). doi:10.1063/1.165949
1993
Cited alongside, same era.
Contopoulos, G., Papadaki, H., Polymilis, C.: The structure of chaos in a potential without escapes. Celest. Mech. Dyn. Astron. 60, 249 (1994). doi:10.1007/BF0069332
1994
Cited alongside, same era.
Siopis, C. V., Contopoulos, G., Kandrup, H. E.: Escape Probabilities in a Hamiltonian with Two Channels of Escape. New York Acad. Sci. Ann. 751, 205 (1995). doi:10.1111/j.1749-6632.1995.tb27523.x
1995
Cited alongside, same era.
Siopis, C. V., Kandrup, H. E., Contopoulos, G., Dvorak, R.: Universal Properties of Escape. New York Acad. Sci. Ann. 773, 221 (1995). doi:10.1111/j.1749-6632.1995.tb12171.x
1995
Cited alongside, same era.
Benet, L., Trautman, D., Seligman, T.: Chaotic Scattering in the Restricted Three-Body Problem. I. The Copenhagen Problem. Celest. Mech. Dyn. Astron. 66, 203-228 (1996). doi:10.1007/BF00054965
1996
Cited alongside, same era.
Siopis, C. V., Kandrup, H. E., Contopoulos, G., Dvorak, R.: Universal properties of escape in dynamical systems. Celest. Mech. Dyn. Astron. 65, 57-681 (1996). doi:10.1007/BF00048438
1996
Cited alongside, same era.
Benet, L., Seligman, T., Trautman, D.: Chaotic Scattering in the Restricted Three-Body Problem II. Small mass parameters. Celest. Mech. Dyn. Astron. 71, 167 (1998). doi:10.1023/A:1008335232601
1998
Cited alongside, same era.
Later among the works it cites.
Apostolatos, T. A., Lukes-Gerakopoulos, G., Contopoulos G.: How to Observe a Non-Kerr Spacetime Using Gravitational Waves. Phys. Rev. Lett. 103, 111101 (2009). doi:10.1103/PhysRevLett.103.111101
2009
Later among the works it cites.
Venegeroles, R.: Universality of Algebraic laws in Hamiltonian Systems. Phys. Rev. Lett., 102, 64101 (2009). doi:10.1103/PhysRevLett.102.064101
2009
Later among the works it cites.
Contopoulos, G., Harsoula, M.: Stickiness effects in chaos. Cel. Mech. Dyn. 107, 77 (2010). doi:10.1007/s10569-010-9282-6
2010
Later among the works it cites.
Lukes-Gerakopoulos, G., Apostolatos, T. A., Contopoulos, G.: Observable signature of a background deviating from the Kerr metric. Phys. Rev. D 81, 124005 (2010). doi:10.1103/PhysRevD.81.124005
2010
Later among the works it cites.
2010
Later among the works it cites.
Bambi, C.: Constraint on the quadrupole moment of super-massive black hole candidates from the estimate of the mean radiative efficiency of AGN. Phys. Rev. D 83, 103003 (2011). doi:10.1103/PhysRevD.83.103003
2011
Later among the works it cites.
Contopoulos, G., Lukes-Gerakopoulos, G., Apostolatos, T. A.: Orbits in a Non-Kerr Dynamical System. Int. J. Bifurc. Chaos 21, 2261 (2011). doi:10.1142/S0218127411029768
2011
Later among the works it cites.