3 papers
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.SP2025
On the Spectra of Sieved Schrödinger Operators
Jake Fillman, Alexandro Luna
We give a family of examples of discrete Schrödinger operators whose spectral dimension is not invariant under sieving. The examples are produced from the Fibonacci Hamiltonian, wh…
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…