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Intermediate Dimensions: A Survey

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Thermodynamic Formalism

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2290))

Abstract

This article surveys the θ-intermediate dimensions that were introduced recently which provide a parameterised continuum of dimensions that run from Hausdorff dimension when θ = 0 to box-counting dimensions when θ = 1. We bring together diverse properties of intermediate dimensions which we illustrate by examples.

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Acknowledgements

The author thanks Amlan Banaji, Stuart Burrell, Jonathan Fraser, Tom Kempton and István Kolossváry for many discussions around this topic. The work was supported in part by an EPSRC Standard Grant EP/R015104/1.

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Authors and Affiliations

  1. Mathematical Institute, University of St Andrews, St Andrews, Fife, UK

    Kenneth J. Falconer

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  1. Kenneth J. Falconer
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Correspondence to Kenneth J. Falconer .

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Editors and Affiliations

  1. Department of Mathematics, Warwick University, Coventry, UK

    Mark Pollicott

  2. Institute de Mathématiques de Toulon, Toulon, France;, Centre de Physique Théorique de Luminy, Marseille, France

    Sandro Vaienti

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Falconer, K.J. (2021). Intermediate Dimensions: A Survey. In: Pollicott, M., Vaienti, S. (eds) Thermodynamic Formalism. Lecture Notes in Mathematics, vol 2290. Springer, Cham. https://doi.org/10.1007/978-3-030-74863-0_14

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