4 problems

The Hofstadter model is a quantum-mechanical model for fermions on a two-dimensional lattice in a magnetic field; its spectrum has a fractal structure, and it is formally related t…

Let $(\infty,\Omega)$ be a quasiperiodic relative fractal drum at infinity, let $\Phi$ denote the geometric inversion, and consider the inverted relative fractal drum…

An irrational vector $\rho\in\mathbb{R}^d$ is Diophantine of class $\beta$ if there exists $C_\beta>0$ such that, for every $k\in\mathbb{Z}^d$ with $k\neq 0$ and every…

Let $T:X\to X$ be a physical dynamical system, and consider its maximal recurrent sets. The conjecture concerns typical, randomly chosen physical systems and the possible kinds of…