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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove that every $C^1$ generic three-dimensional flow has eitherinfinitely many sinks, or, infinitely many hyperbolic or singular-hyperbolicattractors whose basins form a full Lebesgue measure set. We also prove in theorientable case that the set of accumulation points of the sinks of a $C^1$generic three-dimensional flow has no dominated splitting with respect to thelinear Poincar\'e flow. As a corollary we obtain that every three-dimensionalflow can be $C^1$ approximated by flows with homoclinic tangencies or bysingular-Axiom A flows.

Existence of attractors, homoclinic tangencies and singular hyperbolicity for flows