Skip to main content
SpringerLink
Log in

On the measure-preserving mappings with odd dimension

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

In this paper, using two methods: LCN'S (Lyapunov characteristic numbers) method and slice cutting method, we study numerically two mappings with odd dimension:

$$T_1 :\left\{ {\begin{array}{*{20}c} {x_{n + 1} = x_n + z_n ,} \\ {y_{n + 1} = y_n + x_{n + 1} , (\bmod 2\pi )} \\ {z_{n + 1} = z_n + A\sin y_{n + 1} ,} \\ \end{array} } \right. T_2 :\left\{ {\begin{array}{*{20}c} {x_{n + 1} = x_n + y_n + B \sin z_n ,} \\ {y_{n + 1} = y_n + A \sin x_{n + 1} , (\bmod 2\pi ),} \\ {z_{n + 1} = z_n + B \sin y_{n + 1} ,} \\ \end{array} } \right.$$

whereA, B are parameters. For the mappingT 1 the whole region is stochastic; however, we find two-dimensional invariant manifolds for the mappingT 2.

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

  • Arnold, V.: 1976,Méthodes Mathématiques de la Mécanique Classique, Editions Mir. Moscov. p. 290.

    Google Scholar 

  • Arnold, V. I. and Avez, A.: 1967,Problèmes Ergodiques de la Mécanique Classique, Gauthier-Villars, Paris.

    Google Scholar 

  • Benettin, G., Galgani, L., Giorgilli, A., and Strelcyn, J. M.: 1978,Compt. Rend. Acad. Sci. Paris 286A, 431.

    Google Scholar 

  • Benettin, G., Froeschlé, C., Scheidecker, J. P.: 1979,Phys. Rev. A19, 2454.

    Google Scholar 

  • Chirikov, B. V.: 1979,Phys. Reports. 52, 263.

    Google Scholar 

  • Chirikov, B. V., Izraelev, F. M. and Tayurski, V. M.: 1973,Comput. Phys. Commun. 5, 11.

    Google Scholar 

  • Ford, J.: 1973,Adv. Chem. Phys. 24, 155.

    Google Scholar 

  • Ford, J. and Lunsford, G. H.: 1970,Phys. Rev. A1, 59.

    Google Scholar 

  • Froeschlé, C.: 1970,Astron. Astrophys. 9, 15.

    Google Scholar 

  • Hénon, M.: 1969,Quart. Appl. Math. 27, 291.

    Google Scholar 

  • Hénon, M. and Heiles, C.: 1964,Astron. J. 69, 73.

    Google Scholar 

Download references

Author information

Author notes

  1. Yi-Sui Sun

    Present address: Department of Astronomy, University of Nanking, China

Authors and Affiliations

  1. Observatoire de Nice, B.P. 252, 06007, Nice Cedex, France

    Yi-Sui Sun

Authors
  1. Yi-Sui Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, YS. On the measure-preserving mappings with odd dimension. Celestial Mechanics 30, 7–19 (1983). https://doi.org/10.1007/BF01231098

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01231098

Keywords

Search

Navigation