Skip to main content
SpringerLink
Log in

The Lyapunov Spectrum Is Not Always Concave

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We characterize one-dimensional compact repellers having non-concave Lyapunov spectra. For linear maps with two branches we give an explicit condition that characterizes non-concave Lyapunov spectra.

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

  1. Barreira, L., Schmeling, J.: Sets of “non-typical” points have full topological entropy and full Hausdorff dimension. Isr. J. Math. 116, 29–70 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Iommi, G.: Multifractal analysis of Lyapunov exponent for the backward continued fraction map. arXiv:0812.1745

  3. Kesseböhmer, M., Stratmann, B.: A multifractal analysis for Stern–Brocot intervals, continued fractions and Diophantine growth rates. J. Reine Angew. Math. (Crelles J.) 605, 133–163 (2007)

    MATH  Google Scholar 

  4. Parry, W., Pollicott, M.: Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics. Astrisque No. 187–188. Soc. Math. France, Montrouge (1990). 268 pp.

    Google Scholar 

  5. Pesin, Y.: Dimension Theory in Dynamical Systems. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  6. Pesin, Y., Weiss, H.: A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions. J. Stat. Phys. 86(1–2), 233–275 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Przytycki, F., Urbański, M.: Conformal fractals—The ergodic theory methods. Available at http://www.math.unt.edu/~urbanski/pubookpubook0808.pdf

  8. Sarig, O.: Phase transitions for countable Markov shifts. Commun. Math. Phys. 217(3), 555–577 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Walters, P.: An Introduction to Ergodic Theory. Graduate Texts in Mathematics, vol. 79. Springer, Berlin (1981)

    Google Scholar 

  10. Weiss, H.: The Lyapunov spectrum for conformal expanding maps and axiom—A surface diffeomorphisms. J. Stat. Phys. 95(3–4), 615–632 (1999)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile

    Godofredo Iommi & Jan Kiwi

Authors
  1. Godofredo Iommi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Kiwi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Godofredo Iommi.

Additional information

The first author was partially supported by Proyecto Fondecyt 11070050.

Both authors were partially supported by Research Network on Low Dimensional Systems, PBCT/CONICYT, Chile.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Iommi, G., Kiwi, J. The Lyapunov Spectrum Is Not Always Concave. J Stat Phys 135, 535–546 (2009). https://doi.org/10.1007/s10955-009-9750-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-009-9750-0

Keywords

Search

Navigation