MathDBFull-size wild historic set conjecture
Full-size wild historic set conjecture
Consider the class of examples covered by Theorem~, and let the set of wild historic points mean the points with wild historic behavior in those systems.
Full-size wild historic set conjecture. In this class of examples, the set of wild historic points has full Hausdorff dimension, full topological entropy and full topological pressure.
The paper notes that historic sets are known to be geometrically large in many systems, and that related full-pressure results are known under specification-type hypotheses. The asserted simultaneous full Hausdorff-dimension, entropy and pressure conclusion for the stated class is presented as open.
Sources & referencesView supporting material
Primary source
Vitor Araujo and Vilton Pinheiro, “Abundance of wild historic behavior”, arXiv:1609.05356 (2019).
Progress summary
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