Skip to main content
SpringerLink
Log in

Periodic orbits of the generalized Friedmann–Robertson–Walker Hamiltonian systems

  • Original Article
  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

The averaging theory of first order is applied to study a generalization of the Friedmann–Robertson–Walker Hamiltonian systems with three parameters. We provide sufficient conditions on the three parameters of the generalized system to guarantee the existence of continuous families of periodic orbits parameterized by the energy, and these families are given up to first order in a small parameter.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abraham, R., Marsden, J.E.: Foundations of Mechanics. Benjamin, Reading (1978)

    MATH  Google Scholar 

  • Belmonte, C., Boccaletti, D., Pucacco, G.: On the orbit structure of the logarithm potential. Astrophys. J. 669, 202–217 (2007)

    Article  ADS  Google Scholar 

  • Calzeta, E., Hasi, C.E.: Chaotic Friedmann–Robertson–Walker cosmology. Class. Quantum Gravity 10, 1825–1841 (1993)

    Article  ADS  Google Scholar 

  • Hawking, S.W.: Arrow of time in cosmology. Phys. Rev. D 32, 2489–2495 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  • Merritt, D., Valluri, M.: Chaos and mixing in triaxial stellar systems. Astrophys. J. 471, 82–105 (1996)

    Article  ADS  Google Scholar 

  • Page, D.: Will entropy decrease if the universe recollapses? Phys. Rev. D 32, 2496–2499 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  • Papaphilippou, Y., Laskar, J.: Frequency map analysis and global dynamics in a galactic potential with two degrees of freedom. Astron. Astrophys. 307, 427–449 (1996)

    ADS  Google Scholar 

  • Papaphilippou, Y., Laskar, J.: Global dynamics of triaxial galactic models though frequency analysis. Astron. Astrophys. 329, 451–481 (1998)

    ADS  Google Scholar 

  • Pucacco, G., Boccaletti, D., Belmonte, C.: Quantitative predictions with detuned normal forms. Celest. Mech. Dyn. Astron. 102, 163–176 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Verhulst, F.: Nonlinear Differential Equations and Dynamical Systems. Universitext. Springer, Berlin (1996)

    Book  MATH  Google Scholar 

  • Zhao, H.S., Carollo, C.M., De Zeeuw, T.: Can galactic nuclei be non-axisymmetric? The parameter space of power-law discs. Mon. Not. R. Astron. Soc. 304, 457–464 (1999)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The second author is partially supported by the grants MICINN/FEDER MTM 2008–03437, AGAUR 2009SGR410, ICREA Academia and FP7-PEOPLE-2012-IRSES-316338.

Author information

Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Catalonia, Spain

    Jaume Llibre

  2. Department of Mathematics, UBMA University Annaba, Elhadjar, BP12, Annaba, Algeria

    Ammar Makhlouf

Authors
  1. Jaume Llibre
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ammar Makhlouf
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jaume Llibre.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Llibre, J., Makhlouf, A. Periodic orbits of the generalized Friedmann–Robertson–Walker Hamiltonian systems. Astrophys Space Sci 344, 45–50 (2013). https://doi.org/10.1007/s10509-012-1314-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10509-012-1314-0

Keywords

Search

Navigation