Related papers: Foundations of ghost stability
Here we propose a new method to study gravitational stability of the solutions to the Einstein equations. This method uses the canonical superenergy density and it is different from approaches already used (Lyapunov's stability, dynamical…
The inclusion of higher derivatives is a necessary condition for a renormalizable or superrenormalizable local theory of quantum gravity. On the other hand, higher derivatives lead to classical instabilities and a loss of unitarity at the…
Physical experiments and numerical simulations have revealed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper provides a rigorous mathematical justification…
We investigate the classical stability of two coupled scalar fields with opposite-sign kinetic terms evolving in 1+1 dimensional Minkowski spacetime. In the first part, we characterise unquenched ghostly interactions and present numerical…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
The energy in the ghost-free massive gravity theory is calculated via explicitly resolving the initial value constraints for spherically symmetric deformations of flat space. It turns out that the energy is positive in some cases, but in…
We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…
Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…
In this paper, two things are done. (i) First, it is shown that any global symmetry of a gauge-invariant theory can be extended to the ghosts and the antifields so as to leave invariant the solution of the master-equation (before gauge…
A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalised Jacobi equation reformulated for…
In this short note we prove a hierarchical stability result that applies to hybrid dynamical systems satisfying the hybrid basic conditions of (Goebel et al., 2012). In particular, we establish sufficient conditions for uniform asymptotic…
We present a thorough analysis of the cosmological perturbations in Generalised Massive Gravity. This is an extension of de Rham-Gabadadze-Tolley theory where the translation invariance in the St\"uckelberg field space is broken. This…
In this paper we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback asymptotically stabilizes the goal set. Our results rely on novel reduction principles…
This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…
We reconstruct the viable f(G) gravity models from the observations and provide the analytic solutions that well describe our numerical results. In order to avoid unphysical challenges that occur during the numerical reconstruction, we…
We argue that Lee-Wick's complex ghost appearing in any higher derivative theory is stable and its asymptotic field exists. It may be more appropriate to call it ``anti-unstable" in the sense that, the more the ghost `decays' into lighter…
A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…