Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T03:59:56.042Z Has data issue: false hasContentIssue false
  • English
  • Français

Construction d'un difféomorphisme minimal d'entropie topologique non nulle

Published online by Cambridge University Press:  19 September 2008

M. R. Herman
M. R. Herman*
Affiliation:
Centre de Mathématiques de l'Ecole Polytechnique, Palaiseau, France
*
†M. R. Herman, Centre de Mathématiques de l'Ecole Polytechnique, Plateau de Palaiseau, 91128 Palaiseau Cedex, France.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct a real analytic diffeomorphism Fα on a compact connected 4-dimensional manifold M, such that Fα preserves a probability measure μ defined by a smooth volume form, Fα is a minimal diffeomorphism of M and furthermore the metrical entropy of Fα with respect to the measure μ is strictly positive. By a theorem of Goodwyn the topological entropy is also strictly positive. We write down the explicit formula of Fα that depends on a parameter α ∈ T1. This parameter is chosen by Baire category.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 1 , March 1981 , pp. 65 - 76
Copyright
Copyright © Cambridge University Press 1981

References

REFERENCES

[1]Auslander, L., Green, L. & Hahn, F.. Flows on Homogeneous Spaces, Ann. of Math. Studies No. 53. Princeton University Press: Princeton 1963. (Voir aussi dans cette référence, G. A. Hedlund 1.)CrossRefGoogle Scholar
[2]Derriennic, Y.. Sur le théorèeme ergodique sous additif. C. R. Acad. Sc. Paris 281 (1975), 985–988.Google Scholar
[3]Fathi, A. & Herman, M. R.. Existence de difféomorphismes minimaux. Proc. Conf. Systèmes dynamiques, Varsovie (1977), Astérisque 4 (1979), 37–59.Google Scholar
[4]Herman, M. R.. Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Publ.de l'I. H. E. S. 49, (1979), 5–234.Google Scholar
[5]Pesin, J. B.. Characteristic Lyapunov exponents and smooth ergodic theory. Russian Math. Surveys 32 (4) (1977), 55–114.CrossRefGoogle Scholar
[6]Ruelle, D.. Ergodic theory of diflerentiable dynamical systems. Publ. de l'I. H. E. S. 50 (1980), 27–58.Google Scholar
[7]Siegel, C. L.. Topics in Complex Function Theory, vol. 2. Wiley-Interscience: New York, 1971.Google Scholar