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math.DS2025
On the Regularity of the Dimension of Cookie-Cutter-Like Sets
Victor Kleptsyn, Alexandro Luna
We study the Hausdorff and box-counting dimensions of cookie-cutter-like sets formed by sequential dynamics of a finite number of expanding maps. Under some natural conditions, the…
math.DS2025
Regularity of Non-stationary Stable Foliations of Toral Anosov Maps
Alexandro Luna
We consider a sequence of (or ) Anosov maps of the two-dimensional torus that satisfy a common cone condition, and show that if their (respectively, ) norms a…
math.DS2024
Generalized Fiber Contraction Mapping Principle
Alexandro Luna, Weiran Yang
We prove a generalized non-stationary version of the fiber contraction mapping theorem. It was originally used in [HirschPugh70] to prove that the stable foliation of a Anoso…