Skip to main content

Pulsating Stars and Fractals

  • Chapter
Applying Fractals in Astronomy

Part of the book series: Lecture Notes in Physics Monographs ((LNPMGR,volume 3))

Abstract

Fractals are encountered in stellar pulsation theory as attractors, resulting from chaotic dynamics of pulsating stars. We review observational and theoretical investigations of chaotic stellar pulsations with particular emphasis on the physical information they provide about stellar interiors.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Aikawa, T. (1987): Astrophys. Sp. Sc. 139, 281.

    Article  ADS  MathSciNet  Google Scholar 

  • Aikawa, T. (1988): Astrophys. Sp. Sc. 149, 149.

    Article  ADS  Google Scholar 

  • Aikawa, T. (1990): Astrophys. Sp. Sc. 164, 295.

    Article  ADS  MathSciNet  Google Scholar 

  • Antonello, E., Mantegazza, L. (1984): Astron. Astrophys. 133, 52.

    ADS  Google Scholar 

  • Argoul, F., Arnéodo, A. (1984): J. Mech. Th. Appl. 241, 118.

    Google Scholar 

  • Arnéodo, A., Argoul, F., Elezgaray, J, Grasseau, G. (1988): in Proc. Conf. Nonlinear Dynamics, Ed. G.G. Turchetti.

    Google Scholar 

  • Auvergne, M. (1988): Astron. Astrophys. 204, 341.

    ADS  Google Scholar 

  • Auvergne, M., Baglin, A. (1985): Astron. Astrophys. 142, 388.

    ADS  Google Scholar 

  • Auvergne, M., Baglin, A. (1986): Astron. Astrophys. 168, 118.

    ADS  Google Scholar 

  • Auvergne, M., Goupil, M.J., Baglin, A., Serre, T. (1990a): in Fractals in Astronomy, Ed. A. Heck, Vistas Astron. 33, 399.

    Google Scholar 

  • Auvergne, M., Chevreton, M., Belmonte, J., Vauclair, G., Dolez, N., Goupil, M.J. (1990b): in Proc. of 7th Eur. Workshop White Dwarfs, Ed. G. Vauclair (Kluwer Acad. Publ., Dordrecht), in press.

    Google Scholar 

  • Badii, R., Broggi, G., Derighetti, B., Ravani, M., Ciliberto, S., Politi, A., Rubio, M.A. (1988): Phys. Rev. Letters 60, 979.

    Article  ADS  Google Scholar 

  • Baker, N.H. (1966): in Stellar Evolution, Eds. R.F. Stein, A.G.W. Cameron, (Plenum Press, New York), p. 333.

    Google Scholar 

  • Baker, N.H., Moore, D.W., Spiegel, E.A. (1971): Quart. J. Mech. Appl. Math. XXIV, 391.

    Article  Google Scholar 

  • Bergé, P., Pommeau, Y., Vidal, C. (1986): Order within Chaos (Wiley, New York).

    MATH  Google Scholar 

  • Broomhead, D.S., King, G.P. (1986): Physica D 20, 217.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Buchler, J.R. (1985): in Chaos in Astrophysics, NATO ARW C 161 (D. Reidel Publ. Co., Dordrecht), p. 137.

    Google Scholar 

  • Buchler, J.R. (1989): in The Numerical Modeling of Nonlinear Stellar Pulsations, Problems and Prospects, Ed. J.R. Buchler (Kluwer Acad. Publ., Dordrecht), p. 1.

    Google Scholar 

  • Buchler, J.R., Regev, O. (1982): Astrophys. J. 263, 312.

    Article  ADS  Google Scholar 

  • Buchler, J.R., Goupil, M.J. (1984): Astrophys. J. 279, 394.

    Article  ADS  MathSciNet  Google Scholar 

  • Buchler, J.R., Goupil, M.J. (1988): Astron. Astrophys. 190, 137.

    ADS  Google Scholar 

  • Buchler, J.R., Goupil, M.J., Kovács, G. (1987): Phys. Letters 126, 177.

    Article  ADS  Google Scholar 

  • Buchler, J.R., Kovács, G. (1987a): Astrophys. J. 320, L57.

    Article  ADS  Google Scholar 

  • Buchler, J.R., Kovács, G. (1987b): Astrophys. J. 318, 232.

    Article  ADS  Google Scholar 

  • Buchler, J.R., Moskalik, P., Kovács, G. (1990): Astrophys. J. 351, 617.

    Article  ADS  Google Scholar 

  • Cannizzo, J.K., Goodings, D.A., Mattei, J.A. (1990): Astrophys. J. 357, 235.

    Article  ADS  Google Scholar 

  • Christensen-Dalsgaard, J. (1988): Advances in Helio and Asteroseismology, Eds. J. Christensen-Dalsgaard, S. Franden (D. Reidel Publ. Co., Dordrecht), p. 3.

    Google Scholar 

  • Christy, R.F. (1966): Astrophys. J. 144, 108.

    Article  ADS  Google Scholar 

  • Christy, R.F. (1967): Astrophys. J. 145, 337.

    Article  ADS  Google Scholar 

  • Conte, R., Dubois, M. (1987): in Proc. IVth. Workshop Nonlinear Evolution Equations and Dynamical Systems, Ed. J. Leon (World Scientific, Singapore), p. 767.

    Google Scholar 

  • Coullet, P., Spiegel, E. (1983): J. Appl. Math. 43, 776.

    MATH  MathSciNet  Google Scholar 

  • Cox, J.P. (1980a): Theory of Stellar Pulsations (Princeton Univ. Press., Princeton).

    Google Scholar 

  • Cox, J.P. (1980b): in Cepheids: Theory and Observations, Ed. B.F. Madore (Cambridge Univ. Press, Cambridge), p. 126.

    Google Scholar 

  • Cox, J.P., Giuli, R.N. (1968): Principle of Stellar Structures (Gordon and Breach, New York).

    Google Scholar 

  • Cvitanović, P. (1984): Universality in Chaos (Hilger, Bristol).

    MATH  Google Scholar 

  • Dziembowski, W., 1982, Acta Astronomica, 32, 147.

    ADS  Google Scholar 

  • Eckmann, J.P., Ruelle, D. (1982): Rev. Mod. Phys. 57, 617.

    Article  ADS  MathSciNet  Google Scholar 

  • Eckmann, J.P., Oliffson Kamphorst, S., Ruelle, D., Ciliberto S. (1986): Phys. Rev. A 34, 4971.

    Article  ADS  MathSciNet  Google Scholar 

  • Fadeyev, Y.A., Fokin, A. (1985): Astrophys. Sp. Sc. 111, 355.

    ADS  Google Scholar 

  • Farmer, J.D., Ott, E., Yorke, J.A. (1983): Physica D 7, 153.

    Article  ADS  MathSciNet  Google Scholar 

  • Farmer, J.D., Sidorowich, J.J. (1988): in Cter. Nonlinear Studies, Los Alamos Lab. Rep. LA-UR-88-901, 277.

    Google Scholar 

  • Fokin, A. (1990): Astrophys. Sp. Sc. 164, 95.

    Article  ADS  Google Scholar 

  • Glasner, S.A., Buchler, J.R. (1989): in The Numerical Modeling of Nonlinear Stellar Pulsations, Problems and Prospects, Ed. J.R. Buchler (Kluwer Acad. Publ., Dordrecht), p. 109.

    Google Scholar 

  • Goupil, M.J., Auvergne, M., Baglin, A. (1988) Astron. Astrophys. 196, L13.

    ADS  Google Scholar 

  • Goupil, M.J., Auvergne, M., Baglin, A. (1990): in Proc. 7th Eur. Workshop White Dwarfs, Ed. G. Vauclair (Kluwer Acad. Publ., Dordrecht), in press.

    Google Scholar 

  • Grassberger, P., Procaccia, I. (1983): Phys. Rev. A 28, 2591.

    Article  ADS  Google Scholar 

  • Grossmann, A., Kronland-Martinet, R., Morlet, J. (1988): in Wavelets, Eds. J.M. Combes, A. Grossmann, Ph. Tchamitchian (Springer-Verlag, Berlin), p. 2.

    Google Scholar 

  • Guckenheimer, J., Holmes, P. (1983): Nonlinear Oscillations, Dynamical Systems and Bifurcation Theory (Springer-Verlag, New York).

    Google Scholar 

  • Hentschel, H.G.E., Procaccia, I. (1983): Physica D 8, 435.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Iooss, G., Joseph, D.D. (1990): Elementary Stability and Bifurcation Theory (Springer-Verlag, New York).

    MATH  Google Scholar 

  • Kaplan, J.L., Yorke, J.L. (1979): Commun. Math. Phys. 67, 93.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Karp, A.H. (1975): Astrophys. J. 199, 448.

    Article  ADS  Google Scholar 

  • King, S.K., Cox, J.P., Eilers, D.D., Davey, W.R. (1973): Astrophys. J. 182, 859.

    Article  ADS  Google Scholar 

  • Klapp, J., Goupil, M.J., Buchler, J.R. (1985): Astrophys. J. 296, 514.

    Article  ADS  Google Scholar 

  • Kolláth, M. (1990): Monthly Not. Roy. Astron. Soc. 247, 377.

    ADS  Google Scholar 

  • Kovács, G., Buchler, J.R. (1988): Astrophys. J. 334, 971.

    Article  ADS  Google Scholar 

  • Kovács, G., Buchler, J.R. (1989): Astrophys. J. 346, 898.

    Article  ADS  Google Scholar 

  • Kurths, E.N., Ruzmaikin, A.A. (1990): Solar Physics 126, 407.

    Article  ADS  Google Scholar 

  • Ledoux, P., Walraven, Th. (1958): Handbuch der Physik 51, 353.

    ADS  Google Scholar 

  • Lorenz, E.N. (1963): J. of Atm. Sci. 20, 130.

    Article  ADS  Google Scholar 

  • Mandelbrot, B.B. (1974): J. Fluid Mech. 62, 331.

    Article  MATH  ADS  Google Scholar 

  • Mattei, J.A., Cannizzo, J.K., Goodings, D.A. (1990): in Confrontation between Stellar Pulsation and Evolution, Ed. C. Cacciari, G. Clementi, Astron. Soc. Pac. Conf. Series 11, 461.

    Google Scholar 

  • Moore, D.W., Spiegel, E.A. (1966): Astron. Astrophys. 116, 341.

    Google Scholar 

  • Moskalik, P., Buchler, J.R. (1990): Astrophys. J. 355, 590.

    Article  ADS  Google Scholar 

  • Osborne, A.R., Provenzale, A. (1989): Physica D 35, 357.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Ostlie, D.A., Cox, A.N., Cahn, J.H. (1982): in Pulsation in Classical and Cataclismic Variables, Eds. J.P. Cox, C.J. Hansen (Joint Inst. Lab. Astrophys., Boulder), p. 297.

    Google Scholar 

  • Perdang, J. (1985): in Chaos in Astrophysics, NATO ARW C 161, Eds. J.R. Buchler, J.M. Perdang, E.A. Spiegel (D. Reidel Publ. Co., Dordrecht), p. 11.

    Google Scholar 

  • Perdang, J. (1989): in The Numerical Modeling of Nonlinear Stellar Pulsations: Problems and Prospects, Ed. J.R. Buchler (Kluwer Acad. Publ., Dordrecht), p. 333.

    Google Scholar 

  • Perdang, J. (1990a): in Rapid Variability of OB Stars, ESO Workshop, Ed. D. Baade (ESO, Garching-bei-München), in press.

    Google Scholar 

  • Perdang, J. (1990b): in Ecole de Structure Interne 2, eds. A.M. Hubert, E. Schatzman (DASGAL, Obs. Paris), in press.

    Google Scholar 

  • Petersen, J.O. (1973) Astron. Astrophys. 27, 89.

    ADS  Google Scholar 

  • Provost, J., Berthomieu, G. (1990): in Ecole de Structure Interne 2, Eds. A.M. Hubert, E. Schatzman (DASGAL, Obs. Paris), in press.

    Google Scholar 

  • Rössler, O.E. (1976): Phys. Letters 57A, 397.

    ADS  Google Scholar 

  • Saijo, K. (1988): Bull. Nat. Sci. Mus., Tokyo, Ser. E 14, 1.

    Google Scholar 

  • Saijo, K., Watanabe, M. (1987): Bull Nat Sci. Mus., Tokyo, Ser. E 10, 1.

    Google Scholar 

  • Saitou, M., Takeuti, M., Tanaka, Y. (1989): Publ Astron. Soc. Japan 41, 297.

    ADS  Google Scholar 

  • Serre, T., Buchler, J.R., Goupil, M.J. (1990): in Proc. 7th Eur. Workshop White Dwarfs, Ed. G. Vauclair (Kluwer Acad. Publ., Dordrecht), in press.

    Google Scholar 

  • Simon, N. (1988): in Pulsation and Mass Loss in Stars, Eds. R. Stalio, L.A. Willson (Kluwer Acad. Publ., Dordrecht), p. 27.

    Google Scholar 

  • Simon, N. (1990): Monthly Not. Roy. Astron. Soc. 246, 70.

    ADS  Google Scholar 

  • Simon, N., Aikawa, T. (1986): Astrophys. J. 304, 249.

    Article  ADS  Google Scholar 

  • Simon, N., Davis, C.G. (1983): Astrophys. J. 266, 787.

    Article  ADS  Google Scholar 

  • Smith, L.A. (1987): Phys. Letters 133A, 283.

    ADS  Google Scholar 

  • Stellingwerf, R.F. (1972): Astron. Astrophys. 21, 91.

    ADS  Google Scholar 

  • Stellingwerf, R.F. (1975): Astrophys. J. 195, 441.

    Article  ADS  Google Scholar 

  • Stobie, R.S. (1969a): Monthly Not Roy. Astron. Soc. 144, 461.

    ADS  Google Scholar 

  • Stobie, R.S. (1969b): Monthly Not Roy. Astron. Soc. 144, 485.

    ADS  Google Scholar 

  • Stobie, R.S. (1969c): Monthly Not. Roy. Astron. Soc. 144, 511.

    ADS  Google Scholar 

  • Stothers, N.R. (1981): Astrophys. J. 247, 941.

    Article  ADS  Google Scholar 

  • Takens, F. (1980): in Dynamical System and Turbulence, Eds. D.A. Rand, L.S. Young (Springer-Verlag, Berlin), p. 366.

    Google Scholar 

  • Takeuti, M. (1987): Astrophys. Sp. Sc. 136, 129.

    Article  ADS  Google Scholar 

  • Takeuti, M., Aikawa, T. (1981): Sci. Rept Tokohu Univ. 8th Seriee 2, 106.

    ADS  Google Scholar 

  • Tresser, C., Coullet, P., Arnéodo, A. (1980): J. Phys. Letters 41, L243.

    Article  Google Scholar 

  • Tuchman, Y., Sack, N., Barkat, Z.K. (1978): Astrophys. J. 219, 183.

    Article  ADS  Google Scholar 

  • Tuchman, Y., Sack, N., Barkat, Z.K. (1979): Astrophys. J. 234, 217.

    Article  ADS  Google Scholar 

  • Unno, W., Osaki, Y., Ando, H., Saio, H., Shibahashi, H. (1989): Nonradial Oscillations of Stars (Univ. Tokyo Press, Tokyo).

    Google Scholar 

  • Vauclair, G., Goupil, M.J., Baglin, A., Auvergne, M., Chevreton, M. (1989): Astron. Astrophys. 215, L17.

    ADS  Google Scholar 

  • Winget, D. (1990): in Proc. 7th Eur. Workshop on White Dwarfs, Ed. G. Vauclair (Kluwer Acad. Publ., Dordrecht), in press.

    Google Scholar 

  • Winget, D., Van Horn, H.M., Hansen, C.J. (1981): Astrophys. J. 245, L55.

    Article  Google Scholar 

  • Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A. (1985): Physica D 16, 285.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Zlodos, E. (1990): Astrophys. Sp. Sc. 165, 111.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Goupil, MJ., Auvergne, M., Serre, T. (1991). Pulsating Stars and Fractals. In: Heck, A., Perdang, J.M. (eds) Applying Fractals in Astronomy. Lecture Notes in Physics Monographs, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47582-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-47582-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54353-4

  • Online ISBN: 978-3-540-47582-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics