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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Motivated by proving the loss of ergodicity in expanding systems of piecewiseaffine coupled maps with arbitrary number of units, all-to-all coupling andinversion symmetry, we provide ad-hoc substitutes - namely inversion-symmetricmaps of the simplex with arbitrary number of vertices - that exhibit severalasymmetric absolutely continuous invariant measures when their expanding rateis sufficiently small. In a preliminary study, we consider arbitrary maps ofthe multi-dimensional torus with permutation symmetries. Using thesesymmetries, we show that the existence of multiple invariant sets of such mapscan be obtained from their analogues in some reduced maps of a smaller phasespace. For the coupled maps, this reduction yields inversion-symmetric maps ofthe simplex. The subsequent analysis of these reduced maps show that theirsystematic dynamics is intractable because some essential features vary withthe number of units; hence the substitutes which nonetheless capture thecoupled maps common characteristics. The construction itself is based on asimple mechanism for the generation of asymmetric invariant union of polytopes,whose basic principles should extend to a broad range of maps with permutationand inversion symmetries.

Symmetry-breaking-induced loss of ergodicity in maps of the simplex with inversion symmetry