iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://doi.org/10.1007/978-94-009-5468-7_3
Cosmic Arrhythmias | SpringerLink
Skip to main content
Springer Nature Link
Log in

Cosmic Arrhythmias

  • Chapter
Chaos in Astrophysics

Part of the book series: NATO ASI Series ((ASIC,volume 161))

Abstract

Cosmic matter is not stationary. Most of it is probably turbulent. Though we cannot solve even the simple fluid equations that describe such dynamics, many astrophysicists consider that we are progressing by constructing simple models of the phenomena observed. The possibility of making models that have predictive value for some aspects of the observations while ignoring certain of the implications is at the bottom of the success story of the physical sciences. The discussion in this volume is about a variant of such model making, that has some newness about it. We are examining models that are inspired, not so much by the detection of specific physical processes, but by the observation of qualitative kinds of spatial or temporal variability.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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.

Similar content being viewed by others

References

  • Andropov, A.A., Vitt, E.A. and Khaikin, S.E., Theory of Oscillators, Pergamon (1966); original Russian version (1930), translation published by Princeton Press also, but omits Vitt.

    Google Scholar 

  • Arneodo, A., Coullet, P.H., Spiegel, E.A., Turbulence and Chaotic Phenomena in Fluids; edited by T. Tatsumi, North-Holland (1984) 215–220.

    Google Scholar 

  • Arneodo, A., Coullet, P.H., Spiegel, E.A., Geophys. & Astrophys. Fluid Dyn., 31 (1985) 1–48.

    Article  ADS  MATH  Google Scholar 

  • Arneodo, A., Coullet, P.H., Spiegel, E.A. and Tresser, C., Physica, 14D (1985) 327–347.

    MathSciNet  ADS  Google Scholar 

  • Arneodo, A., Coullet, P. and Tresser, C., J. Stat. Phys. 27 (1982) 171–182.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Arnold, V.I., Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, Grundlagen der mathematischen Wissenschaften 250 (1983).

    MATH  Google Scholar 

  • Auvergne, M. in Instabilities Hydrdynamiques et Applications Astrophysiques, A. Baglin, ed., Soc. Francais des Specialités d’Astronomie (1983) 319–333.

    Google Scholar 

  • Auvergne, M., Baglin, A. and Morel, P.-J., Astron. & Astrophys., 104 (1981) 47–56.

    ADS  Google Scholar 

  • Baker, N.H., in Stellar Evolution, R.F. Stein and A.G.W. Cameron, eds., Plenum Press (1976).

    Google Scholar 

  • Baker, N.H., Moore, D.W., and Spiegel, E.A., Astron. J., 9 (1966) Abstract.

    Google Scholar 

  • Bergé, P., Pomeau, Y. and Vidal, C., L’Ordre dans le Chaos, Hermann, Paris (1984).

    Google Scholar 

  • Bretherton, C.S. and Spiegel, E.A., Phys. Lett., 96A (1983) 152–156.

    ADS  Google Scholar 

  • Buchler, R. and Perdang, J., Astrophys. J., 231 (1979) 524.

    Article  ADS  Google Scholar 

  • Defouw, R.J., Astrophys. J., 160 (1970) 659.

    Article  ADS  Google Scholar 

  • Carr, J., Applications of Centre Manifold Theory, Springer-Verlag, Applied Mathematical Sciences 35 (1981).

    Google Scholar 

  • Celnikier, L.M., Astronomy and Astrophysics, 60 (1977) 421–422.

    ADS  Google Scholar 

  • Childress, S. and Fautrell, Y., Geophys. & Astrophys. Fluid Dyn., 22 (1982) 235–279.

    Article  ADS  MATH  Google Scholar 

  • Childress, S. and Spiegel, E.A., in Variations of the Solar Constant, S. Sofia, ed. NASA Conference Pub. 2191 (1980) 273–292.

    Google Scholar 

  • Coullet, P.C. and Spiegel, E.A., SIAM J. Appl. Math., 43 (1983) 775–819.

    Article  MathSciNet  Google Scholar 

  • Deubner, F.-L., Ulrich, R.K. and Rhodes, E.J., Jr., Astron. Astrophys., 72 (1979) 177.

    ADS  Google Scholar 

  • Drazin, P.G. and Reid, W.H. Hydrodynamic Stability, Camb. Univ. (1981).

    Google Scholar 

  • Eddy, J.A., Science, 192 (1976) 1189.

    Article  ADS  Google Scholar 

  • Edmonds, A.R., Angular Momentum in Quantum Mechanics, Princeton University Press (1957) p. 26.

    Google Scholar 

  • Evans, J.W. and Michard, R., Astrophys. J., 136 (1962) 493–506.

    Article  ADS  Google Scholar 

  • Fowler, A., Sudies in Applied Math. (1984) 215–233.

    Google Scholar 

  • Friedman, B., Principles and Techniques of Applied Mathematics, John Wiley and Sons (1956).

    Google Scholar 

  • Gilmore, R., Catastrophe Theory for Scientists and Engineers, Wiley & Sons (1981).

    Google Scholar 

  • Guckenheimer, J. & Holmes, P., Nonlinear Oscilllations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, Applied Math. Sciences 42 (1981).

    Google Scholar 

  • Gudzenko, L.I and Chertoprud, V.E., in The Kinematics of Simple Models in the Theory of Oscillations, N.G. Basov, ed., Proc. P.N. Lebedev Physics Institute, 90 (1976); English Version Published by Consultants Bureau of Plenum Press (New York, 1978) Chapt. VIII, 153–199.

    Google Scholar 

  • Haken, H., Synergetics. An Introduction. Nonequilibrium Phase Transitions in Physics, Chemistry and Biology. Springer-Verlag (1977).

    Google Scholar 

  • Hao, B.-L., Chaos, World Scientific Pub. Co. (1984).

    Google Scholar 

  • Hayashi, H., Ishizuka, S., Hirakawa, K., Phys. Lett., 98A (1983) 474–476.

    ADS  Google Scholar 

  • Izenman, A.J., Math. Intelligencer, 7 (1985) 27–33.

    Article  MathSciNet  MATH  Google Scholar 

  • Jeans, J.H., Astronomy and Cosmogony, Camb. Univ. (1928) p. 193.

    Google Scholar 

  • Lamb, H., Proc. Roy. Soc. A l(1907) 170.

    Google Scholar 

  • Lebovitz, N.R. and Schaar, R.J., Studies in applied Math., LIV (1975) 229–260.

    Google Scholar 

  • Leibacher, J.W. and Stein, R.F. in the Sun as a Star, S. Jordan, ed., NASA SP-450 (1981) 263–287.

    Google Scholar 

  • Lewin, W.G.H. and Joss, P.C., Space Sci. Rev., 29 (1981) 3–87.

    Article  ADS  Google Scholar 

  • Lorenz, E.N., Jour. Atmos. Sci., 20 (1963) 130–141.

    Article  ADS  Google Scholar 

  • Malkus, W.V.R., Trans. Am. Geophys. Union, 53 (1972) 617.

    Google Scholar 

  • Mandelbrot, B.B., The Fractal Geometry of Nature, Freeman (1983).

    Google Scholar 

  • Marzec, C.J. and Spiegel, E.A., SIAM J. App. Math., 38 (1980) 403–421.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • McLaughlin J.B. and Orszag, S.A., J. Fluid Mech., 122 (1982) 123–142.

    Article  ADS  MATH  Google Scholar 

  • Moon, H.T., Huerre, P. and Redekopp, L.G., Phys. Rev. Lett., 49 (1982) 458.

    Article  MathSciNet  ADS  Google Scholar 

  • Moore, D.R., Toomre, J., Knobloch, E. and Weiss, N.O., Nature, 303 (1983) 663–667.

    Article  ADS  Google Scholar 

  • Moore D.W. and Spiegel, E.A., Astrophys. J., 143 (1966) 871–887.

    Article  MathSciNet  ADS  Google Scholar 

  • Newell, A.C., Envelope Equations, Lectures in Applied Math., 15 (1974) 157–163.

    MathSciNet  Google Scholar 

  • Newell, A.C. and Whitehead, J.A., J. Fluid Mech., 38 (1969) 279–303.

    Article  ADS  MATH  Google Scholar 

  • Parker, E.N., Cosmical Magnetic Fields, Oxford (1979).

    Google Scholar 

  • Pomeau, Y., in Nonlinear Dynamics and Turbulence, G.I. Barenblatt, G. Iooss and D.D. Joseph, eds. Pitman (1983) 295–304.

    Google Scholar 

  • Press, W.H., Comments on Astrophys., 7 (1978) 103–119.

    ADS  Google Scholar 

  • Robbins, K.A., SIAM J. Applied Math., 36 (1979) 457–472.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Rutten, R.J. and Cram, L.E. in the Sun as a Star, S. Jordan, ed., NASA SP-450 (1981) 3–10.

    Google Scholar 

  • Ruzmaikin, A.A., Comments on Astrophys., 9 (1981) 85–96.

    ADS  Google Scholar 

  • Schuster, H.G., Deterministic Chaos, Physik-Verlag, Weinheim (1984).

    MATH  Google Scholar 

  • Segel, L.A., J. Fluid Mech., 38 (1969) 203–224.

    Article  ADS  MATH  Google Scholar 

  • Shapiro, S.L. and Teukolsky, S.A., Black Holes, White Dwarfs and Neutron Stars, Wiley-Interscience (1983).

    Google Scholar 

  • Shil’nikov, L.P., Math. Sbornik 6 (1968) 427–438.

    Article  Google Scholar 

  • Sparrow, C., The Lorenz Equations:Bifurcations, Chaos and Strange Attractors, Applied Math Sciences 41, Springer-Verlag (1982).

    Google Scholar 

  • Spiegel, E.A., Convection in Stars II. Special Effects, Ann. Rev. Astron. & Astrophys. (1972) 261–304.

    Google Scholar 

  • Spiegel, E.A., in Problems of Stellar Convection, E.A. Spiegel and J.-P. Zahn, eds., Lecture Notes in Physics 71, Springer-Verlag (1977) p.3.

    Google Scholar 

  • Spiegel, E.A., Ann. N.Y. Acad. Sci., 357 (1980) 305–312.

    Article  ADS  Google Scholar 

  • Spiegel, E.A. and Weiss, N.O., Nature, 287 (1980) 616.

    Article  ADS  Google Scholar 

  • Steiner, J.M., Bull. Aust. Math. Soc., 9 (1973) 153–154; and Thesis, Math. Dept., Monash Univ. (1973).

    Google Scholar 

  • Unno, W., Osaki, Y., Ando, H. and Shibahashi, H., Nonradial Oscillations of Stars, University of Tokyo Press, (1978).

    Google Scholar 

  • Weiss, N.O., Cattaneo, F., Jones, C.A., Geophys. & Astrophys. Fluid Dyn. (1984).

    Google Scholar 

  • Wesfried, J.E. and Zaleski, S., eds., Cellular Structures in Instabilities, Lecture Notes in Physics 210, Springer-Verlag (1984).

    Google Scholar 

  • Wolf, A., Swift, J.B., Swinney, H.L. and Vastano, J.A., Physica D (1985) in press.

    Google Scholar 

Download references

Authors
  1. E. A. Spiegel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Physics Department, University of Florida, Gainesville, USA

    J. R. Buchler

  2. Astrophysical Institute, Liège, Belgium

    J. M. Perdang

  3. Astronomy Department, Columbia University, New York, USA

    E. A. Spiegel

Rights and permissions

Reprints and permissions

Copyright information

© 1985 D. Reidel Publishing Company, Dordrecht, Holland

About this chapter

Cite this chapter

Spiegel, E.A. (1985). Cosmic Arrhythmias. In: Buchler, J.R., Perdang, J.M., Spiegel, E.A. (eds) Chaos in Astrophysics. NATO ASI Series, vol 161. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5468-7_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-5468-7_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8914-2

  • Online ISBN: 978-94-009-5468-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation