Real Analysis Exchange

Measures of maximal dimension for linear horseshoes.

Michał Rams

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Abstract

We consider a linear Smale-William's' horseshoe with different contraction/dilatation coefficients and find equilibrium states of maximal Hausdorff dimension. We compute this dimension and show an example when the state of maximal dimension is non-unique.

Article information

Source
Real Anal. Exchange, Volume 31, Number 1 (2005), 55-62.

Dates
First available in Project Euclid: 5 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149516807

Mathematical Reviews number (MathSciNet)
MR2218188

Zentralblatt MATH identifier
1096.37013

Subjects
Primary: 37D35: Thermodynamic formalism, variational principles, equilibrium states
Secondary: 28D20: Entropy and other invariants

Keywords
hyperbolic maps Smale's horseshoe ergodic measures measures of maximal dimension

Citation

Rams, Michał. Measures of maximal dimension for linear horseshoes. Real Anal. Exchange 31 (2005), no. 1, 55--62. https://projecteuclid.org/euclid.rae/1149516807


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References

  • K. Falconer, Fractal Geometry, Mathematical Foundations and Applications, John Wiley and Sons, Chichester, 1995.
    Mathematical Reviews (MathSciNet): MR2118797
  • A. Manning, H. McCluskey, Hausdorff dimension for horseshoes, Erg. Th. and Dyn. Sys., 3 (1983), 251–260.
    Mathematical Reviews (MathSciNet): MR742227
    Digital Object Identifier: doi:10.1017/S0143385700001966

Michigan State University Press

Real Analysis Exchange

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