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 analyze the dynamics of a class of cosmological solutions of theEinstein-Vlasov equations. These equations describe an ensemble ofcollisionless particles (which represent galaxies or clusters of galaxies) thatinteract gravitatively through Einstein's equations of general relativity. Thecosmological models we consider are spatially homogeneous, of Bianchi type IX,and locally rotationally symmetric (LRS). We prove that generic solutionsexhibit an oscillatory approach toward the singularities (the "big bang" in thepast and the "big crunch" in the future); this is in contrast to the behaviorof Einstein-vacuum or Einstein-Euler solutions. To establish this result wemake use of dynamical systems theory; we introduce dimensionless dynamicalvariables that are defined on a compact state space; in this formulation theoscillatory behavior of generic solutions is represented by an approach toheteroclinic cycles.

Oscillations toward the singularity of LRS Bianchi type IX cosmological models with Vlasov matter