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

We prove that, for a $C^\infty$-generic contact form $\lambda$ adapted to agiven contact distribution on a closed three-manifold, there exists a sequenceof periodic Reeb orbits which is equidistributed with respect to $d\lambda$.This is a quantitative refinement of the $C^\infty$-generic density theorem forthree-dimensional Reeb flows, which was previously proved by the author. Theproof is based on the volume theorem in embedded contact homology (ECH) byCristofaro-Gardiner, Hutchings, Ramos, and inspired by the argument ofMarques-Neves-Song, who proved a similar equidistribution result for minimalhypersurfaces. We also discuss a question about generic behavior of periodicReeb orbits "representing" ECH homology classes, and give a partial affirmativeanswer to a toy model version of this question which concerns boundaries ofstar-shaped toric domains.

Equidistributed periodic orbits of $C^\infty$-generic three-dimensional Reeb flows