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

Miquel dynamics is a discrete time dynamics for circle patterns. Previouswork shows that the circle centers satisfy the dSKP equation on the octahedrallattice $A_3$ and give rise to a real-valued Y-system / cluster structure. Inthis article we show that half the intersection points satisfy the dSKPequation as well, and we introduce two new real-valued Y-systems for Miqueldynamics that involve only the intersection points. Therefore, the newY-systems are M\"obius invariant. We also show that the circle centers andintersection points combined satisfy the dSKP equation on the 4-dimensionaloctahedral lattice $A_4$. In addition, we present two more complex-valuedY-systems for Miquel dynamics, which are real-valued in and only in the case ofintegrable circle patterns. We also show that in the case of harmonicembeddings, the old and the new Y-patterns coincide.

M\"obius invariant Y-systems (cluster structures) for Miquel dynamics