PreprintarXiv licencearXiv
Stable manifolds of heteroclinic chains in Hořava-Lifshitz cosmology
Abstract
We consider vacuum spatially homogeneous models in Hořava-Lifshitz gravity, which are expected to describe generic singularities for these modified gravity theories. These models perturb the well-known Bianchi models in general relativity (GR) by a parameter v∈ (0,1), in which GR occurs at v=1/2. We show that all periodic heteroclinic chains of Bianchi type II orbits are robust for small perturbations of GR, i.e. they exist for any v≈ 1/2. Moreover, we prove the existence of a stable manifold for each heteroclinic chain within a Cantor set for the supercritical case, v∈ (1/2,1). In particular, we discuss the heteroclinic chains of periods three and four in detail.
Related
- Conditional Stable Laws and Rare-Event Limits for Absorbing Markov Chains
- Stable constant mean curvature disks with circular boundary in homogeneous three-manifolds
- Smooth Limits of Stable Manifolds
- Links and singularities of stable maps from $3$-manifolds to surfaces
- Boundary behaviour of stable Allen-Cahn limit-interfaces in Riemannian manifolds
BibTeX
@misc{sprink2026stable,
title = {{Stable manifolds of heteroclinic chains in Hořava-Lifshitz cosmology}},
author = {Hauke Sprink and Phillipo Lappicy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18283},
eprint = {2610.18283},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18283},
}
RIS
TY - UNPB
TI - Stable manifolds of heteroclinic chains in Hořava-Lifshitz cosmology
AU - Hauke Sprink
AU - Phillipo Lappicy
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18283
UR - https://arxiv.org/abs/2610.18283
AB - We consider vacuum spatially homogeneous models in Hořava-Lifshitz gravity, which are expected to describe generic singularities for these modified gravity theories. These models perturb the well-known Bianchi models in general relativity (GR) by a parameter v∈ (0,1), in which GR occurs at v=1/2. We show that all periodic heteroclinic chains of Bianchi type II orbits are robust for small perturbations of GR, i.e. they exist for any v≈ 1/2. Moreover, we prove the existence of a stable manifold for each heteroclinic chain within a Cantor set for the supercritical case, v∈ (1/2,1). In particular, we discuss the heteroclinic chains of periods three and four in detail.
ER -