5 papers
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…
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…
On the Spectrum of Sturmian Hamiltonians of Bounded Type in a Small Coupling Regime
Alexandro Luna
We prove that the Hausdorff dimension of the spectrum of a discrete Schrödinger operator with Sturmian potential of bounded type tends to one as coupling tends to zero. The proof…
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, w…
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…