We characterize all quasiperiodic Sturmian words: a Sturmian word is not quasiperiodic if and only if it is a Lyndon word. Moreover, we study links between Sturmian morphisms and quasiperiodicity.

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of t...

A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor. For weak interactions between atoms, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the con...

The stable magnetisation configurations of antiferromagnets on quasiperiodic tilings are investigated theoretically. The exchange coupling is assumed to decrease exponentially with the distance between magnetic moments. It is demonstrated that the combination of geometric frustration and the quasiperiodic order of atoms leads to complicated noncollinear ground states. The structure can be divid...

Title of dissertation: QUASIPERIODICITY AND CHAOS Suddhasattwa Das, Doctor of Philosophy, 2015 Dissertation directed by: Professor James A. Yorke Department of Mathematics In this work, we investigate a property called “multi-chaos” is which a chaotic set has densely many hyperbolic periodic points of unstable dimension k embedded in it, for at least 2 different values of k. We construct a fami...

Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium. Specifically, we show that the interplay of symmetry breaking and localization in the quasiperiodic quantum Ising chain produces a quasiperiodic Ising glass s...

On April 8, 1982, Dan Shechtman conducted an electron diffraction experiment on aluminum/manganese alloy. The pattern showed tenfold symmetry although the rules of crystallography excluded such in extended structures. Alan L. Mackay had anticipated structures, which fit his view generalized crystallography. persisted claiming to have observed quasiperiodic structures despite denial even by Linu...

As an absolute invariant of smooth conjugacy, the multiplier group described the types of space-time symmetries that the flow has, and for a quasiperiodic flow on the n-torus, is the determining factor of the structure of its generalized symmetry group. It is conjectured that a quasiperiodic flow is F -algebraic if and only if its multiplier group is a finite index subgroup of the group of unit...