Hasselblatt–Schmeling dimension conjecture for hyperbolic sets
Hasselblatt–Schmeling dimension conjecture for hyperbolic sets
Let a hyperbolic set have stable and unstable slices, and interpret “fractal dimension” as either Hausdorff dimension or upper box dimension. Hasselblatt–Schmeling conjecture. The fractal dimension of a hyperbolic set is the sum of the fractal dimensions of its stable and unstable slices, for either choice of fractal dimension. This conjecture concerns the additivity of dimensions along the stable and unstable directions of hyperbolic dynamics; the supplied source does not state whether it has been resolved.
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Sources & referencesView supporting material
Primary source
Ricardo Bortolotti and Eberson Ferreira da Silva, “Dimension of a class of intrinsically transversal solenoidal attractors in high dimensions”, arXiv:2205.05437 (2022).
Additional references
2 papers in this index state this conjecture (2020–2022). The statement above is taken from the most recent of them; the others are arXiv:2003.08926.
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