1999/09/30 by Awadhesh Prasad, Ramakrishna Ramaswamy, Indubala I. Satija +1 · 1 citation
Materials Science · Physics and Astronomy · #Quantum chaos and dynamical systems #Quasicrystal Structures and Properties #Theoretical and Computational Physics #chao-dyn #nlin.CD
paper · pdf · doi:10.1103/physrevlett.83.4530
published as Phys.Rev.Lett.83:4530,1999 · To be appear in Physical Review Letters
arxiv created 1999/09/30 · openalex publication_date 1999/11/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Strange nonchaotic attractors (SNAs) can be created due to the collision of an invariant curve with itself. This novel ``homoclinic'' transition to SNAs occurs in quasiperiodically driven maps which derive from the discrete Schr"odinger equation for a particle in a quasiperiodic potential. In the classical dynamics, there is a transition from torus attractors to SNAs, which, in the quantum system, is manifest as the localization transition. This equivalence provides new insight into a variety of properties of SNAs, including its fractal measure. Further, there is a symmetry breaking associated with the creation of SNAs which rigorously shows that the Lyapunov exponent is nonpositive. We show that these characteristics associated with the appearance of SNA are robust and occur in a large class of systems.