Abstract
We have seen in the previous chapters the impact of the presence of chaos in a given dynamical system. Furthermore, we have seen the importance of assessing the predictability of a given model through the use of the finite-time Lyapunov exponent distributions.
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Notes
- 1.
Indeed, only in 1942 the German mathematician Carl Siegel could show the convergence for one series of these characteristics.
References
Boyd, P.T., Mindlin, G.B., Gilmore, R., Solari, H.G.: Topological analysis of chaotic orbits: revisiting Hyperion. Astrophys. J. 431, 425 (1994)
Breeden, J.L.: Chaos in core oscillations of globular clusters. Astrophys. J. 448, 672 (1995)
De Bruyne, V., Leewin, F., Dejonghe, H.: Approximate third integrals for axisymmetric potentials using local stackel fits. Mon. Not. R. Astron. Soc. 311, 297 (2000)
Buchler, J.T., Goupil, M.J.: A mechanism for the irregular variability of supergigant stars. Astron. Astrophys. 190, 137 (1988)
Cannizo, J.K., Goodings, D.A.: Chaos in SS cygni? Astrophys. J. 334, L31 (1988)
Compte, A.: The Positive Philosophy, Book II, Chapter 1. George Bell and Sons, London (1842)
Contopoulos, G.: Order and Chaos in Dynamical Astronomy. Springer, Berlin (2002)
Contopoulos, G., Vandervoort, P.O.: A rotating Staeckel potential. Astrophys. J. 389, 118 (1992)
Correia, A.C.M., Laskar, J.: Lon-term evolution of the spin of Venus: II numerical simulations. Icarus 163, 24 (2003)
Dvorak, R.: Numerical results to the Sitnikov-problem. Celest. Mech. Dyn. Astron. 56, 7180 (1993)
Edvardsson, S., Karlsson, K.G.: Spin axis variations of Mars: numerical limitations and model dependencies. Astron. J. 135, 1151 (2008)
Hanslmeier, A., Brajsa, R.: The chaotic solar cycle: I analysis of cosmogenic 14C-data. Astron. Astrophys. 509, A5 (2010)
Harding, A.K., Shinbrot, T.: A chaotic attractor in timing noise from the Vela pulsar. Astrophys. J. 353, 588 (1990)
von Hoerner, S.: Die numerische integration des n-Körper-Problemes für Sternhaufen. I. Z. Astroph. 50, 184 (1960)
Holmberg, E.: On the clustering tendencies among the nebulae. II. A study of encounters between laboratory models of stellar systems by a new integration procedure. Astrophys. J. 94, 385 (1941)
Hubble, E.: Extragalactic nebulae. Astrophys. J. 64, 321 (1926)
Kirchhoff, G.: Ueber die Fraunhofer’schen Linien (On Fraunhofer’s lines), Monatsbericht der Kniglichen Preussische Akademie der Wissenschaften zu Berlin (Monthly report of the Royal Prussian Academy of Sciences in Berlin), 662–665 (1859)
Kiss, L.L., Szatmary, K.: Period-doubling events in the light curve of R Cygni: evidence for chaotic behaviour. Astron. Astrophys. 390, 585 (2002)
Kollath, Z., Buchler, J.R., Serre, T., Mattei, J.: Analysis of the irregular pulsations of AC Herculis. Astron. Astrophys. 329, 147 (1998)
Konig, M., Timmer, J.: Analysing X-ray variability by linear state space models. Astron. Astrophys. Suppl. Ser. 124, 589 (1997)
Kovacs, T., Erdi, B.: Transient chaos in the Sitnikov problem. Celest. Mech. Dyn. Astron. 105, 289 (2009)
Kovacs, T., Bene, G.Y., Tel, T.: Relativistic effects in the chaotic Sitnikov problem. Mon. Not. R. Astron. Soc. 414, 2275 (2011)
Laskar, J., Joutel, F., Robutel, P.: Stabilization of the Earth’s obliquity by the Moon. Nature 361, 615 (1993)
Laughlin, G., Chambers, J.E.: Extrasolar Trojans: the viability and detectability of planets in the 1:1 resonance. Astron. J. 600, 124 (2002)
Lawrence, A., Papadakis, I.: X-ray variability of active galactic nuclei: a universal power spectrum with luminosity dependent amplitude. Astrophys. J. 414, L85 (1993)
Lehto, H.J., Mc Hardy, I.M.: AGN X-ray light curves -shot noise or low dimensional attractor? Mon. Not. R. Astron. Soc. 261, 125 (1993)
Lochner, J.C., Swank, J.H., Szymkowiak, A.E.: A search for a dynamical attractor in Cygnus X-1. Astrophys. J. 337, 823 (1989)
MacMillan, W.D.: An integrable case in the restricted problem of three bodies. Astrophys. J. 27, 11 (1911)
Magnenat, P.: Asymptotic orbits and instability zones in dynamical systems. Astron. Astrophys. 77, 332 (1979)
Mannatil, M., Gupta, H., Chakraborty, S.: Revisiting evidence of chaos in X-Ray light curves: the case of GRS1915+105. Astrophys. J. 833, 208 (2016)
Merrit, D., Fridman, T.: Triaxial galaxies with cusps. Astrophys. J. 460, 136 (1996)
Mikkola, S., Innanen, K.: Solar system chaos and the distribution of asteroid orbits. Mon. Not. R. Astron. Soc. 277, 497 (1995)
Milankovitch, M.: Canon of insolation and the ice-age problem (Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitenproblem). Academie royale serbe, Editions speciales, 132 Belgrad (1941)
Moore, G.E.: Cramming more components onto integrated circuits. Electronics 38, 114–117 (1965)
Moser, J.: Stable and random motion in dynamical systems. Ann. Math. Stud. 77, 199 (1973)
Muller, P., Dvorak, R.: A survey of the dynamics of main belt asteroids. Astron. Astrophys. 300, 289 (1995)
Orzaru, C.M.: On the dimension of the solar activity attractor. IAUS 157, 910 (1993)
Pfenniger, D.: Numerical study of complex stability. Astron. Astrophys. 150, 97 (1985)
Poincaré, H.: On the three-body problem and the equations of dynamics. Acta Math. 13, 1 (1890)
Qin, Z.: A nonlinear prediction of the smoothed monthly sunspot numbers. Astron. Astrophys. 310, 646 (1996)
Regev, O.: Chaos and Complexity in Astrophysics. Cambridge University Press, New York (2006)
Ritcher, P.H.: Harmony and complexity: order and chaos in mechanical systems. Lecture on “The emergence of complexity in Mathematics, Physics, Chemistry and Biology” Plenary session of the Pontifical Academy of Sciences, Rome (October 1992)
Roy, A.E.: Orbital Motion. Ed. Adam Hilger, Bristol (1982)
Serre, T., Kollath, Z., Buchler, J.R.: Search for low dimensional nonlinear behavior in irregular variable stars. Astron. Astrophys. 311, 833 (1996)
Seymour, A.D., Lorimer, D.R.: Evidence for chaotic behaviour in pulsar spin-down rates. Mon. Not. R. Astron. Soc. 428, 983 (2013)
Sitnikov, K.: The existence of oscillatory motions in the three-body problems. Dokl. Akad. Nauk. USSR 133, 303 (1960)
Sitnikov, K.: The existence of oscillatory motions in the three-body problem. Sov. Phys. Dokl. 5, 647 (1961)
Springel, V.: The cosmological simulation code GADGET-2. Mon. Not. R. Astron. Soc. 364, 1105 (2005)
Sukova, P., Grzedzielski, M., Janiuk, J.: Chaotic and stochastic processes in the accretion flows of the black hole X-ray binaries revealed by recurrence analysis. Astron. Astrophys. 586, A143 (2016)
Timmer, J., Schwarz, U., Voss, H.U., Kurths, J.: Linear and nonlinear time series analysis of the black hole candidate Cygnus X-1. Phys. Rev. E 61, 1342 (2000)
Varvoglis, H., Voyatzis, G., Scholl, H.: Spectral analysis of asteroidal trajectories in the 2:1 resonance. Astron. Astrophys. 300, 591 (1995)
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Vallejo, J.C., Sanjuan, M.A.F. (2019). Chaos, Predictability and Astronomy. In: Predictability of Chaotic Dynamics . Springer Series in Synergetics. Springer, Cham. https://doi.org/10.1007/978-3-030-28630-9_5
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