Measures of maximal dimension for linear horseshoes.

Michał Rams

doi:rae/1149516807

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Home > Journals > Real Anal. Exchange > Volume 31 > Issue 1 > Article

2005-2006 Measures of maximal dimension for linear horseshoes.

Michał Rams

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Michał Rams¹
¹Institute of Mathematics, Polish Academy of Sciences

Real Anal. Exchange 31(1): 55-62 (2005-2006).

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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.

References

K. Falconer, Fractal Geometry, Mathematical Foundations and Applications, John Wiley and Sons, Chichester, 1995. MR2118797 K. Falconer, Fractal Geometry, Mathematical Foundations and Applications, John Wiley and Sons, Chichester, 1995. MR2118797

A. Manning, H. McCluskey, Hausdorff dimension for horseshoes, Erg. Th. and Dyn. Sys., 3 (1983), 251–260. MR742227 10.1017/S0143385700001966 A. Manning, H. McCluskey, Hausdorff dimension for horseshoes, Erg. Th. and Dyn. Sys., 3 (1983), 251–260. MR742227 10.1017/S0143385700001966

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Michał Rams "Measures of maximal dimension for linear horseshoes.," Real Analysis Exchange 31(1), 55-62, (2005-2006). https://doi.org/

Published: 2005-2006

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