English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider uniformly (DC) or periodically (AC) driven generalized infiniteelastic chains (a generalized Frenkel-Kontorova model) with gradient dynamics.We first show that the union of supports of all the invariant measures, denotedby A, projects injectively to a dynamical system on a 2-dimensional cylinder.We also prove existence of ergodic invariant measures supported on a set ofrotationaly ordered configurations with an arbitrary (rational or irrational)rotation number. This shows that the Aubry-Mather structure of ground statespersists if an arbitrary AC or DC force is applied. The set A attracts almostsurely (in probability) configurations with bounded spacing. In the DC case,the set A consists entirely of equilibria and uniformly sliding solutions. Thekey tool is a new weak Lyapunov function on the space of translationallyinvariant probability measures on the state space, which counts intersections.

The Aubry-Mather theorem for driven generalized elastic chains