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Chaos in variable stars: topological analysis of W Vir model pulsations. (English) Zbl 1055.85500

Summary: The topological characterization of chaos is applied to the irregular pulsations of a model for a star of the W Virginis type, computed with a state-of-the-art numerical hydrodynamical code. The banded W Vir attractor is found to possess an additional twist when compared to the Rössler band. It is shown that the stellar light-curve contains the same dynamical information about the attractor as the stellar radius or as the radial velocity variations.

MSC:

85A15 Galactic and stellar structure
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
85-08 Computational methods for problems pertaining to astronomy and astrophysics
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
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References:

[1] Buchler J. R., Astrophy. J. Lett. 320 pp L57– (1987) · doi:10.1086/184976
[2] Kovács G., Astrophys. J. 334 pp 971– (1988) · doi:10.1086/166890
[3] Buchler J. R., Ann. N.Y. Acad. Sci. 617 pp 17– (1990) · doi:10.1111/j.1749-6632.1990.tb37794.x
[4] DOI: 10.1103/PhysRevLett.45.712 · doi:10.1103/PhysRevLett.45.712
[5] Mindlin G. B., Phys. Rev. Lett. 64 pp 2350– (1990) · Zbl 1050.37509 · doi:10.1103/PhysRevLett.64.2350
[6] DOI: 10.1016/0375-9601(76)90101-8 · Zbl 1371.37062 · doi:10.1016/0375-9601(76)90101-8
[7] Birman J. S., Topology 22 pp 47– (1983) · Zbl 0507.58038 · doi:10.1016/0040-9383(83)90045-9
[8] Melvin P., Phys. Rev. A 44 pp 3419– (1991) · doi:10.1103/PhysRevA.44.R3419
[9] Letellier C., Chaos 5 pp 271– (1995) · Zbl 1270.37006 · doi:10.1063/1.166076
[10] DOI: 10.1088/0951-7715/7/3/008 · Zbl 0806.58015 · doi:10.1088/0951-7715/7/3/008
[11] DOI: 10.1103/PhysRevE.51.164 · doi:10.1103/PhysRevE.51.164
[12] Fang H. P., Phys. Rev. E 49 pp 5025– (1994) · doi:10.1103/PhysRevE.49.5025
[13] Cvitanović P., Phys. Rev. A 38 pp 1503– (1988) · doi:10.1103/PhysRevA.38.1503
[14] Milnor J., Lect. Notes Math. 1342 pp 465– (1988) · doi:10.1007/BFb0082847
[15] Le Sceller L., Phys. Rev. E 49 pp 4693– (1994) · doi:10.1103/PhysRevE.49.4693
[16] Mindlin G. B., J. Nonlinear Sci. 1 pp 147– (1991) · Zbl 0797.58057 · doi:10.1007/BF01209064
[17] Serre T., Astron. Astrophys. 311 pp 833– (1986)
[18] Serre T., Astron. Astrophys. 311 pp 845– (1986)
[19] DOI: 10.1016/0167-2789(92)90085-2 · Zbl 0761.62118 · doi:10.1016/0167-2789(92)90085-2
[20] Grassberger P., J. Phys. A 22 pp 5217– (1989) · Zbl 0722.58016 · doi:10.1088/0305-4470/22/24/011
[21] Fang H. P., J. Phys. A 28 pp 3901– (1995) · Zbl 0860.58014 · doi:10.1088/0305-4470/28/14/011
[22] DOI: 10.1103/PhysRevLett.74.842 · doi:10.1103/PhysRevLett.74.842
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