Periodic orbits in Ho\v{r}ava-Lifshitz cosmologies
| Autor: | Kevin E. M. Church, Olivier Hénot, Phillipo Lappicy, Jean-Philippe Lessard, Hauke Sprink |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Spatially homogeneous models
Physics and Astronomy (miscellaneous) Mathematics - Classical Analysis and ODEs Hořava–Lifshitz cosmology 500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik Periodic orbits Mathematics - Dynamical Systems Computer-assisted proofs General Relativity and Quantum Cosmology Mathematical Physics |
| Popis: | We consider spatially homogeneous Ho\v{r}ava-Lifshitz (HL) models that perturb General Relativity (GR) by a parameter $v\in (0,1)$ such that GR occurs at $v=1/2$. We describe the dynamics for the extremal case $v=0$, which possess the usual Bianchi hierarchy: type $\mathrm{I}$ (Kasner circle of equilibria), type $\mathrm{II}$ (heteroclinics that induce the Kasner map) and type $\mathrm{VI_0},\mathrm{VII_0}$ (further heteroclinics). For type $\mathrm{VIII}$ and $\mathrm{IX}$, we use a computer-assisted approach to prove the existence of periodic orbits which are far from the Mixmaster attractor and thereby we obtain a new behaviour which is not described by the BKL picture of bouncing Kasner-like states. Comment: 21 pages, 7 figures. arXiv admin note: text overlap with arXiv:2012.07614 |
| Databáze: | OpenAIRE |
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