The laminations of a crystal near an anti-continuum limit

Vincent Knibbeler, Blaz Mramor, Bob Rink

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

The anti-continuum limit of a monotone variational recurrence relation consists of a lattice of uncoupled particles in a periodic background. This limit supports many trivial equilibrium states that persist as solutions of the model with small coupling. We investigate when a persisting solution generates a so-called lamination and prove that near the anti-continuum limit the collection of laminations of solutions is homeomorphic to the (N - 1)-dimensional simplex, with N the number of distinct local minima of the background potential. This generalizes a result by Baesens and MacKay on twist maps near an anti-integrable limit.
Original languageEnglish
Pages (from-to)927-952
JournalNonlinearity
Volume27
Issue number5
DOIs
Publication statusPublished - May 2014

Fingerprint Dive into the research topics of 'The laminations of a crystal near an anti-continuum limit'. Together they form a unique fingerprint.

Cite this