The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation
properties quite distinct from those appearing in continuous nonlinear systems. For a large …

We comment on some recent investigations on the electronic properties of models
associated with the Thue-Morse chain, point out that their conclusions contradict rigorously …

Trace maps of two-letter substitution rules are investigated with special emphasis on the
underlying algebraic structure and on the existence of invariants. We illustrate the results …

3.2. 2. Explaining the fragmentation scheme 3.2. 3. Energy spectra via information entropy
3.2. 4. Energy spectrum robustness. 3.3. Energy spectrum in aperiodic superlattices 3.3. 1 …

We study the emergence of quasiperiodic Bloch wave functions in quasicrystals, employing
the one-dimensional Fibonacci model as a test case. We find that despite the fact that Bloch …

In the following pages we discuss infinite sequences defined on a finite alphabet, and more
specially those which are generated by finite automata. We have divided our paper into …

One-dimensional quasiperiodic systems are often based on an inflation rule giving rise to a
recursion formula on the transfer matrices. It is shown in a general setting, that the norm …

We study Schrödinger operators on the real line whose potentials are generated by an
underlying ergodic subshift over a finite alphabet and a rule that replaces symbols by …

The continuous Schrödinger equation is discussed for the Fibonacci chain and its
generalizations and compared to the tight-binding approximation. For Kronig-Penney like …

We study tunneling of Dirac particles through Kronig-Penney models on general lattices,
computing their transmission coefficient. We subsequently focus our attention on the …