Geodesic
Piecewise contracting maps on the interval: Hausdorff dimension, entropy, and attractors
Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 318-327

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DOI

We consider the attractor $\Lambda $ of a piecewise contracting map f defined on a compact interval. If f is injective, we show that it is possible to estimate the topological entropy of f (according to Bowen’s formula) and the Hausdorff dimension of $\Lambda $ via the complexity associated with the orbits of the system. Specifically, we prove that both numbers are zero.
DOI : 10.4153/S0008439523000747
Mots-clés : Interval map, piecewise contraction, attractor, complexity, Hausdorff dimension 
Calderón, Alfredo E.; Villar-Sepúlveda, Edgardo. Piecewise contracting maps on the interval: Hausdorff dimension, entropy, and attractors. Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 318-327. doi: 10.4153/S0008439523000747
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     title = {Piecewise contracting maps on the interval: {Hausdorff} dimension, entropy, and attractors},
     journal = {Canadian mathematical bulletin},
     pages = {318--327},
     year = {2024},
     volume = {67},
     number = {2},
     doi = {10.4153/S0008439523000747},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000747/}
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